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]
How many times larger is 5 × 10 to the power of 6 than 5 × 10 to the power of 2?
Answer:
10,000
Step-by-step explanation:
The bases of the scientific notation are the same, so the answer must be a base of 10. So you just divide [tex]10^{6}[/tex] and [tex]10^{2}[/tex], you should get [tex]10^{4}[/tex], which is equal to 10,000.
Oh yikes this is a hard one!
Divide and answer in simplest form
A. 1/15
B. 15/1
C. 3/5
D. 5/3
Answer:
A.
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] ÷ 5 = [tex]\frac{1}{3}*\frac{1}{5} =\frac{1}{15}[/tex]
please help me people thank you in advance
Answer:
[tex]-\dfrac{11}{12}[/tex]
Step-by-step explanation:
[tex]\dfrac{\dfrac{5}{8}+\dfrac{3}{4}}{\dfrac{-2}{3}-\dfrac{5}{6}}=\\\\\\\dfrac{\dfrac{11}{8}}{-\dfrac{9}{6}}=\\\\\\\dfrac{11}{8}\times -\dfrac{2}{3}=\\\\\\-\dfrac{22}{24}=\\\\\\-\dfrac{11}{12}[/tex]
Hope this helps!
Consider the following simplified algebraic expression. 10 x squared y + 6 x squared minus 7 y squared minus 6 Which could be the original expression? 8 x squared y + 7 x squared minus 5 y squared + 3 x minus 2 + 2 x squared y minus x squared minus 2 y squared + 3 x minus 4 8 x squared y + 7 x squared minus 5 y squared + 3 x minus 2 + 2 x squared y minus x squared minus 2 y squared minus 3 x minus 4 8 x squared y + 7 x squared minus 5 y squared + 3 x + 2 + 2 x squared y minus x squared minus 2 y squared minus 3 x minus 4 8 x squared y + 7 x squared minus 5 y squared + 3 x minus 2 minus 2 x squared y minus x squared minus 2 y squared minus 3 x minus 4
9514 1404 393
Answer:
(b) 8x^2y +7x^2 -5y^2 +3x -2 +2x^2y -x^2 -2y^2 -3x -4
Step-by-step explanation:
Detailed comparison of the answer choices seems to be required. The x^2y terms need to sum to 10x^2y, the 3x terms need to cancel, the constant terms need to sum to -6.
The appropriate choice on this list appears to be the second choice.
_____
Comment on the problem
In the form presented, it takes considerable time to sort the answer choices from one another and to determine what their differences are. It would be much more conducive to getting an answer if the problem were presented using the usual math symbols in a form that separates the question and the different answer possibilities.
Answer:
B
Step-by-step explanation:
i am smart
Question 10 Multiple Choice Worth 1 points)
(01.03 LC)
Jamie has 105 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 7 kids on her block. Write an equation to show how many pieces of candy each kid
will recele.
Answer:
105= 7x or 7x=105 x=15
Step-by-step explanation:
Hope this helps
Correct me if this is wrong
A jar of quarters and dimes contains $20.00. There are 110 coins in all. How many of each are there?
Answer:
There are 50 dimes and 110-50 = 60 quarters in the collection.
Step-by-step explanation:
Let D be the number of dimes.
Then the number of quarters is (110-D).
The "value equation" is
10D + 25*(110-D) = 2000.
Simplify and solve for D:
10D + 2750 - 25D = 2000,
-15D = 2000 - 2750,
-15D = -750,
D = %28-750%29%2F%28-15%29 = 50.
Elise says, "If you subtract 16 from my number and multiply the difference by - 7, the result is
-154” what is Elise’s number?
Answer:
-6
Explanation:
Elise's number is x.
If you subtract 16 from her number -> x-16
and multiply the difference by 7 -> 7(x-16) = -154
Elise's number is -154/7+16 = -6
What is the mean of 12, 24, 24, and 52
Answer:
Mean = 28
Step-by-step explanation:
Mean = [tex]\frac{sum of observations}{number of observations}[/tex]
Mean = [tex]\frac{12+24+24+52}{4}[/tex]
Mean = [tex]\frac{112}{4}[/tex]
Mean = 28
What is the product?
(negative 3 s + 2 t)(4 s minus t)
negative 12 s squared minus 2 t squared
negative 12 s squared + 2 t squared
negative 12 s squared + 8 s t minus 2 t squared
negative 12 s squared + 11 s t minus 2 t squared
Answer:
[tex] \boxed{- 12 {s}^{2} + 11st - 2 {t}^{2} } [/tex]
Step-by-step explanation:
[tex] = > ( - 3s + 2t)(4s - t) \\ \\ = > - 3s(4s - t) + 2t(4s - t) \\ \\ = > ( ( - 3s) \times 4s )- (( - 3s) \times t) + (2t \times 4s) - (2t \times t) \\ \\ = > - 12 {s}^{2} - ( - 3st) + 8st - 2 {t}^{2} \\ \\ = > -12 {s}^{2} + 3st + 8st - 2 {t}^{2} \\ \\ = > - 12 {s}^{2} + 11st - 2 {t}^{2} [/tex]
Penny wrote the mixed number 4 2/7 as 8/7. Describe Penny's error, and EXPLAIN how she should of have written the improper fraction
Answer:
She must have multiplied 4 times 2/7 which is 8/7. She should have written it as 30/7.
Step-by-step explanation:
shoulders knees and toes ♀️✨♀️♀️wait i forgot the head,, thats what you'll get later✨♀️♀️♀️✨✨♀️♀️✨✨
sorry i just needed to put something here
Answer:
C
Step-by-step explanation:
-3x - 2 ≥ 7
-3x ≥ 9
x ≤ -3
Answer:
c
Step-by-step explanation:
-3x-2 greater than or equal to 7
-3x greater than or equal to 9
x less than or equal to -3
(flip the inequality sign if you multiply by a negative number on both sides)
c
A rectangular prism and a square pyramid were joined to form a composite figure.
A rectangular prism with a length of 9 inches, width of 9 inches, and height of 5 inches. A square pyramid with triangular sides with a base of 9 inches and height 4 inches.
[Not drawn to Scale]
What is the surface area of the figure?
261 in.2
333 in.2
405 in.2
477 in.2
Answer:
B. 333 in.2
Step-by-step explanation:
The area of the base is 81^2
lateral is 45 x 4 = 180^2 (9x5x4)
180^2 add the 72 pyramid = 252^2 + base of 81^2 = 333^2
Composite figueres i do like this as shown to you a few seconds ago.
The triangle shows us just the height
4 inches
We can see that height is smaller central isosceles height across the center base point.
We also can remember to use the length 9inches but divide by 2 and get each triangle area this way.
4 x 1/2 base = 4x 1/2 4.5 = 4 x 2.25 = 9^2 each right side triangle
9 x 8 = 72^2
we add the areas 72+ 81+lateral 180 = 333 inches^2
Answer:
it is B
I took the quiz
A girl flying a kite lets out 130 feet of string that makes an angle of 52° with the ground. If the string forms a straight line, how high is the kite above the ground? Hint: Draw a picture (triangle) and label. 80.04 feet 102.44 feet 166.39 feet 164.97 feet
Answer:
The height of the kite above the ground is 102 .44 feet
Step-by-step explanation:
To find the height of the kite above the ground, we will follow the steps below:
let h represent the height of the kite above the ground
we will use trigonometric ratio to solve
SOH CAH TOA
sinФ = opposite/hypotenuse
cosФ=adjacent / hypotenuse
tanФ=opposite / adjacent
from the diagram below
opposite = h
hypotenuse = 130 feet
Ф = 52°
The best trig ratio to use is sin
sin Ф = opposite / hypotenuse
sin52° = h / 130
cross-multiply
h = 130 sin 52°
h=102.44°
The height of the kite above the ground is 102 .44 feet
Help please I need the answer
____________________________________
Hey!!
Solution,
Diameter (d)=17 cm
Radius(r)=17/2=8.5 cm
Circumference of circle=?
Now,
Circumference of circle=2 pi r
=2*3.14*8.5
=53.38 cm
The right answer is 53.4cm
Hope it helps
Good luck on your assignment
_________________________________
Help mee pweaseeeeeee :)))
Answer: .4
Step-by-step explanation:
.
I would like to know how to solve this please.
Can you help me with this?
|a^2| if a<0
Answer:
|(-a)²| = | a² | = a²
Step-by-step explanation:
absolute value is always positive number as well as any number squared so sign is positive no matter what
will mark bianleast
When figure ABCD is reflected across the dotted line into figure A′B′C′D', which describes the position of B'?
5 units below the dotted line
5 units above the dotted line
3 units below the dotted line
3 units above the dotted line
Answer:
5 units above the dotted line
Step-by-step explanation:
The reason for this is that there is a distance of 5 units between point B and the line so we know that when it is reflected there will be a distance of 5 as well.
What principal will amount to $3000 if invested at 3% interest compounded
semiannually for 10 years?
Please show the work of the problem
Answer: $2227.41
Step-by-step explanation:
A = P(1 + r/n)^nt
Find the measure of the largest angle in the diagram below. (Type the
number only).
Answer: 112
2x+3x+10=180
5x=170
x=34
3x+10=112
The measure of the largest angle in the diagram is 112 degrees.
What is Angle?An angle is formed when two straight lines or rays meet at a common endpoint.
The sum of two angles is 180 degrees when they are complementary.
2x+3x+10=180
Two times of x plus three times of x plus ten equal to one hundred eighty.
5x+10=180
Five times of x plus ten equal to one hundred eighty.
Subtract 10 from both the sides
5x=170
Divide both sides by 5
x=34
Now substitute x value in 3x+10 which is largest angle.
3(34)+10
102+10
112
Hence, the measure of the largest angle in the diagram is 112 degrees.
To learn more on Angles click:
https://brainly.com/question/28451077
#SPJ2
Need Help ASAP!!!!!....
this is khan academy and i need it fast thx
Answer:
C
Step-by-step explanation:
The angles are supplementary because all the angles add up to 180 and they form a straight line together.
HELP WILL GIVE BRAINLIEST!!!!
How many 1/2 cups are in 3/4 cups?
Answer:
1 1/2 or 1.5
Step-by-step explanation:
think: half of 4 is 2 so 1 half cup would make it to 2/4
than half of that is 1/4 which is 1/2 of 1/2 a cup
adding that to 2/4 makes it 3/4 so therefore... (Peep the answer)
I NEED HELP ASAP :(
Use the distributive property to write the sum as a product.
(-1)·2+(-1)·ₓ
Answer:
−2 − x
Step-by-step explanation:
Answer:
-2-x
Step-by-step explanation:
distribute the the like terms and separate the problem then solve it.
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
Help asap PLEASE, dhdbhehf
Answer:
3
Step-by-step explanation:
Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal. In this example, these are two pairs of Alternate Interior Angles: 2 and 3
Given:
AB || DE
C is the midpoint of BD
Prove:
C is the midpoint of AE
Answer:
Step-by-step explanation:
Given: AB║DE and C is the midpoint of BD.
To prove: C is the midpoint of A
Statements Reasons
1). AB║DE 1). Given
2). BC ≅ CD 2). Point C is the midpoint of BD
3). m∠B ≅ m∠D 3). Interior alternate angles
4). m∠ACB ≅ m∠DCE 4). Vertical angles
5). ΔABC ≅ ΔDEC 5). ASA property of congruence
6). AC ≅ EC 6). ΔABC ≅ ΔDEC
7). AC = [tex]\frac{1}{2}(\text{AE})[/tex] 7). AC ≅ EC
How many 6 packs of soda do jace and jake need to buy if each person has one soda?
Answer:
3 6 pks are required
Step-by-step explanation:
There are 14 people at the party
14 = 6x where x is the number of 6 pks
Divide each side by 6
14/6 = 6x/6
2 1/3 = x
Since we cannot buy part of a 6 pk, we round up
3 6 pks are required
Simplify the following 2a + 3b + 4a – 7b
Answer:2a
We add 2 and 3 and we get 5 then we do 4-7=-3. Then we do 5-3=2 and we add a.(we only add all a’s when we multiply)
And the answer is 2a
63 people are going to the zoo. There are 3 cars to take people to the zoo. How
many will go in each car if the same number go in each car?
Answer:
21
3x21= 63 have a great day
Step-by-step explanation:
BRAINLIEST PLEASE