Chloe has enough sand to fill a sandbox with an extra area of 36 square units she wants the outer edge of the sandbox to use as little as Material possible
Answer:
[tex]Length = Width = 6\ units[/tex]
Step-by-step explanation:
Given
[tex]Area=36[/tex]
Required
The least possible material
Sandboxes usually, are rectangles or squares.
Using the above assumption, the area is calculated as:
[tex]Area= Length * Width[/tex]
[tex]Area= L* W[/tex]
[tex]L * W = 36[/tex]
Make L the subject
[tex]L = \frac{36}{W}[/tex]
The material of the outer edge is calculated by the perimeter.
[tex]Perimeter = 2 * (L +W)[/tex]
[tex]P = 2 * (L + W)[/tex]
Substitute [tex]L = \frac{36}{W}[/tex]
[tex]P = 2 * (\frac{36}{W} + W)[/tex]
Open bracket
[tex]P = \frac{72}{W} + 2W[/tex]
[tex]P = 72W^{-1} +2W[/tex]
To get the minimum material needed, we differentiate P
[tex]P' = -72W^{-2} + 2[/tex]
Set: [tex]P' = 0[/tex]
[tex]-72W^{-2} + 2 = 0[/tex]
Collect like terms
[tex]72W^{-2} = 2[/tex]
Divide both sides by 72
[tex]W^{-2} = \frac{2}{72}[/tex]
[tex]W^{-2} = \frac{1}{36}[/tex]
Rewrite as:
[tex]\frac{1}{W^2} = \frac{1}{36}[/tex]
Take positive square roots of both sides
[tex]\frac{1}{W} = \frac{1}{6}[/tex]
Cross multiply
[tex]W = 6[/tex]
Recall that: [tex]L = \frac{36}{W}[/tex]
So, we have:
[tex]L =\frac{36}{6}[/tex]
[tex]L = 6[/tex]
Hence, the dimension with the littlest material as possible is:
[tex]Length = Width = 6\ units[/tex]
Artem drives 12.6 miles in 12 minutes.
He passes a sign which gives the speed limit as 50 mph.
By how much, in mph, did Artem's average speed exceed the speed limit?
Answer:
18 mph
Step-by-step explanation:
12.6 × 5 =68.0. 68 - 50 = 18
write an equivalent expression in standard form.
(2x + 5)(x + 1)
The equivalent expression in standard form is 2x² + 7x + 5.
What is Expression?An expression is combination of variables, numbers and operators.
To write the expression in standard form, we need to simplify it by multiplying the two factors using the distributive property of multiplication:
(2x + 5)(x + 1) = 2x² + 2x + 5x + 5
Combining like terms, we get:
(2x + 5)(x + 1) = 2x² + 7x + 5
Therefore, the equivalent expression in standard form is 2x² + 7x + 5.
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Given circle B below, find the value of x.
A 27
B 44
C 71
D 142
Answer:
B. 44°
Step-by-step explanation:
Central angle = 3x + 10°
Inscribed angle = 2x - 17°
Now
Central angle = 2 * inscribed angle
( Central angle is double of the inscribed angle standing on same arc)
3x + 10° = 2 ( 2x - 17°)
3x + 10° = 4x - 34°
4x - 3x = 34 ° + 10°
x = 44°
Hope it will help :)❤
can someone help me with this because I am struggling and if you don't mind show me the steps
6 to the negative 4th power times 6 to the 7th power
Answer:
216
Step-by-step explanation:
(6 to the -4th) * (6 to the 7th)
Which of the following is equivalent to the expression shown below
Answer:
v^3/2
Step-by-step explanation:
(sqrt(v))^3
sqrt(v)^3
v^3/2
Jenny counted the coins in her bank.
She had 4 times as many nickels as dimes.
She had 8 more quarters than nickels.
She had 52 dimes.
How many quarters did Jenny have in her bank?
A.
21
B.
64
C.
200
D.
216
Answer:
Step-by-step explanation:
its d cause there is actually 208 nickles and if u ad 8 more it gives u 216.
Answer: D.
Step-by-step explanation:
52x4=208
Since we know she has 4 times as many nickels as dimes(52), we just have to multiply 52x4 to get 208 nickels
208+8=216
We know that she has 8 more quarters than nickels(208) so we have to add 8 to 208 to get 216 quarters
I hope this helps
Hopefully it's brainlist
-2 (4d-1)=26 how to solve plz
Answer:
-3 = D
Step-by-step explanation:
A really smart freind of mine says this is the answer.
anyone know the answer?
helpppp me pleaaaaseeeewww
Answer:
A
Step-by-step explanation:
I believe it is A If I remember correctly
Write the standard form of the equation of the circles that passes through (0, 3) with its center at (0,0)
Answer:
[tex]x^2+y^2=9[/tex]
Step-by-step explanation:
Equation of a circle (when centred at the origin):
[tex]x^2+y^2=r^2[/tex] where r is the radius of the circle
Plug in the point (0,3) to solve for the radius squared
[tex]0^2+3^2=r^2\\9=r^2[/tex]
Plug r² back into the original equation
[tex]x^2+y^2=9[/tex]
I hope this helps!
End of Module 4 Assessment
Answer:
where's the question?
Step-by-step explanation:
is it a question?
Answer:
whats the question?
Step-by-step explanation:
I have a 30% off Kohl’s coupon!!! I find a pair of jeans for $29. What would my cost be with the 30% off?
Answer:
$20.30 plus tax
Step-by-step explanation:
You multiply 28 x .30 and that is your discount.
Answer:
$20.30
Step-by-step explanation:
(2-1/2)(3-1/3)(4-1/4)
Answer: 1/4
Step-by-step explanation:
2-1/2 ==> 1/2
3-1/3 ==> 2/3
4-1/4 ==> 3/4
1/2 x 2/3 x 3/4 = 6/24
*Reduce 6/24*
1/4
What is the factored form of 12x²-48?
answer this question!!! :)
Answer:
X = 1
Step-by-step explanation:
You first divide each side by 3 leaving you with X+5 = 6. Then you take the 5 to the other side leaving you with X=6-5 as the 5 changes from positive to negative. So 6-5=1 so X=1
Hope this helped
-A3miz
Age:13
HELP ME NOW PLEASE................
If the square below is enlarged by a scale factor of 2, what will be the area of the new square? 184 square units 188 square units 192 square units 196 square units
Answer:
256square units
Step-by-step explanation:
Since we are not given a diagram. Let us assume the side length of the given square is 8 units
If the the square is enlarged by a scale factor of 2, the side length of the new square will be 2 * 8 = 16units
Since area of a square = L²
Hence the area of the new square = 16²
area of the new square = 256 square units
Hence the area of the new square is 256square units
Note that the side length of the original square was assumed. The values can change depending on the side length of the original square before enlargement
Emily is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 3 people. Emily booked a total of 15 rooms which can accommodate 36 guests altogether. Graphically solve a system of equations in order to determine the number of small rooms reserved,
Answer: 9.
Step-by-step explanation:
6 large rooms which will add up to 18
9 small rooms which will also add up to 18 totaling the 36 guests.
The no. of small and large rooms in the hotel are 9 and 6 respectively.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, Emily is blocking off several rooms in a hotel for guests coming to her wedding.
Let us assume that small rooms be x and large rooms to be y.
Emily booked a total of 15 rooms which is x + y = 15...(i).
which can accommodate 36 guests altogether which is 2x + 3y = 36...(ii)
Now if we multiply eqn(i) by 2 it'll be 2x + 2y = 30...(iii)
Now subtracting eqn(iii) from eqn(ii) we get y = 6.
substituting the value of y in eqn(iii) we get x = 9.
So, the number of small rooms is 9 and no. of large rooms is 6.
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how many solutions does 2(4x+5)=8x+8
Answer:
Step-by-step explanation:
Its no soluction.
Which of the following is equivalent to
4x2y - 2y2x - 5xy
Select one:
a. -2x2y - 5xy + 4xy2
b. 2xy2 - 5xy + 4x2y
c. -2xy2 + 5xy + 4x2y
d. -2xy2 - 5xy + 4x2y
e. 2x2y - 5xy
Answer:
1 Simplify 4x\times 2y4x×2y to 8xy8xy.
8xy-2y\times 2x-5xy
8xy−2y×2x−5xy
2 Simplify 2y\times 2x2y×2x to 4yx4yx.
8xy-4yx-5xy
8xy−4yx−5xy
3 Simplify.
-xy
−xy
Step-by-step explanation:
Solve. 382.04 – 6.3 *
Help
7 11 10
3 8 2 . 0 4
- 6 . 3
------------------
3 7 5 . 7 4
Answer:
375.74
Step-by-step explanation:
The explanation are in the picture.
Please explain the answer and real answers only. Find the y=mx+b
Answer:
-2
Step-by-step explanation:
Given equation
x - 2y = 4
2y = x - 4
y = ( x - 4 ) / 2
y = x/2 - 4 /2
y = x/2 - 2
Comparing with y = mx + b
y-intercept (b) = - 2
Hope it will help :)❤
Find the diameter of a circle with a circumference of 63 feet. Round your answer to the nearest hundredth.
The diameter is about__
feet.
Answer:
20.05feet
Step-by-step explanation:
Given data
Circumference= 63feet
The expression for circumference is
C= 2πr
substitute
63= 2*3.142*r
63= 6.284r
r= 63/6.284
r=10.025
Hence the diameter is
=10.025*2
=20.05feet
Mallory works 20 hours a week as a website designer and earns $42.50 per hour. If Mallory saves
1
2
of her total website-design earnings each week, how much will she save in 4 weeks?
Answer:
I believe it's 17000
Step-by-step explanation:
42.50 x 20 = 850
850 x 5 (5 business days) = 4250
4250 x 4 (4 weeks) = 17000
When Larry tried to teach his dog Allegra to speak, he gave him 1 sausage - and he barked once. When he
gave him 2 sausages, he barked twice. Then he gave him 3 sausages, and he barked three times.
Larry predicted that Allegra would bark four times if he gave him 4 sausages.
What type of reasoning did Larry use to make his prediction?
A. Deductive reasoning
B. Inductive reasoning
C. Indirect reasoning
D. Circular reasoning
In case of : Allegra barking n = 4 times, when given 4 sausages - Inductive Logic is used.
Given : Allegra barks once & twice & thrice, when Larry gives him 1 & 2 sausages respectively.
So, later he assumes that he would bark 4 times, if given four sausages
Deductive Reasoning is when conclusion related to particular is drawn, based on general universal. Eg : All men are mortal, Ram is a man. Ram is mortal. Inductive Reasoning is when a generalised conclusion is drawn, based on specific case. Eg : Law of gravity based on apple falling. Allegra's case of barking n times for n sausages (1, 2,3 ...) is further generalised for other positive numbers & hence 4. Indirect Reasoning relates two events. If A is true leads to B is true, then B is false implies A has also been false. Circular Reasoning is a logical fallacy of beginning with an already assumed true statement.To learn more, refer https://brainly.com/question/2848937?referrer=searchResults
When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis
Answer:
For a function f(x), a reflection across the y-axis is written as:
g(x) = f(-x)
While a reflection across the x-axis is written as:
g(x) = -f(x)
So, if the negative sign is outside the transformation, like in:
g(x) = -f(x + 2) - 8
We can conclude that this is a reflection over the x-axis.
While if the "x" inside the function has a negative sign, like in:
g(x) = 5*f(-x + 4) - 3
The reflection is over the y-axis.
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Answer: 4 black marbles, 3 blue, 2 green, and one red.
Step-by-step explanation:
Leo is constructing a tangent line from point Q to circle P. What is his next step?
Mark the point of intersection S of the segment created from the arcs and circle R, and construct line RS.
Mark the point of intersection S of circles R and P, and construct line QS.
Construct arcs from point Q that are greater than half the length of segment PQ.
Construct a circle from point P that has a radius of P and the intersection of circles P and R.
Answer:
hello your question has a missing diagram attached below is the missing diagram
answer :
Mark the point of intersection S of circles R and P, and construct line QS ( option 2 )
Step-by-step explanation:
when constructing a tangent line from one point ( lets say Q as seen in the question ) to a circle P. The next step should be to mark a point of intersection between the given circles and then construct a line through it
Answer:
Mark the point of intersection S of circles R and P, and construct line QS.
Step-by-step explanation:
This is correct because after you create circle R that intersects circle p, you're supposed to mark the intersection points. If your in FLVS, it would be in lesson 7.04. I also got this right on my test. Good luck!