Answer:
I believe the ans is
A ⋂ B = { 6, 12 }
Explanation :
The set operation intersection contains only the elements that are in both set
A ⋂ B
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]
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 :)❤
It is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number greater than 7
What is the probability
Answer:
5 / 8
Step-by-step explanation:
Total possible outcomes = (1, 2, 3, 4, 5, 6, 7, 8)
Odd outcomes = (1, 3, 5, 7)
Outcomes > 7 = 8
Required outcomes = (1, 3, 5, 7, 8)
Number of required outcomes = 5
P(pointer stops on odd or number > 7) = required outcome / Total possible outcomes
P(pointer stops on odd or number > 7) :
= 5 / 8
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!
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)
Plzzzzzzzzz helpppppppppoopoooo
Answer:
a. x = 180 - (j + k)
b.
j + k = (5x - 2) + (2x - 2) = 7x - 4
l = x
x = 180 - (7x - 4)
x = 180 - 7x + 4
8x = 184
x = 184/8
x = 23
l = 23°
j = 5x - 2
j = 5 × 23 - 2
j = 115 - 2
j = 113°
k = 2x - 2
k = 2 × 23 - 2
k = 46 - 2
k = 44°
or k = 180 - (23 + 113) = 180 - 136 = 44°
Dan invests £1200 into his bank account.
He receives 5% per year compound interest.
How much will Dan have after 5 years?
Give your answer to the nearest penny where appropriate.
Answer:
£1500
Step-by-step explanation:
If Dan starts out with £1200 and he gets 5% per year compound interest you would multiply 1200×0.05 and get 60, this is the amount of money that was collected with interest every year. Now you need to multiply 60×5 and get 300. With the total interest over 5 years we need to add the interest and the original amount which would be 1200+300=1500.
A projectile is fired vertically upward, and its height s(t) in feet after t seconds is given by the function s(t)=-16t^2+600t+800. After how many seconds, to the nearest tenth, will the projectile hit the ground?
Answer:
The projectile will hit the ground after 38.8 seconds.
Step-by-step explanation:
You know that the height s (t) in feet of the projectile after t seconds is given by the function
s(t) = - 16t² + 600t + 800.
To know the time at which the projectile will hit the ground, you must replace s(t) by height 0:
0=- 16t² + 600t + 800
This is a quadratic function of the form ax2 + bx + c, where a= -16, b=600 and c=800.
To solve a quadratic function, you must apply the expression:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]
In this case:
[tex]x1,x2=\frac{-600+-\sqrt{600^{2}-4*(-16)*800 } }{2*(-16)}[/tex]
Solving:
[tex]x1,x2=\frac{-600+-\sqrt{360000+51200 } }{-32}[/tex]
[tex]x1,x2=\frac{-600+-\sqrt{411200 } }{-32}[/tex]
[tex]x1,x2=\frac{-600+-641.25 }{-32}[/tex]
So:
[tex]x1=\frac{-600+641.25 }{-32}[/tex]
[tex]x1=\frac{41.25 }{-32}[/tex]
x1= -1.289 seconds
and
[tex]x2=\frac{-600-641.25 }{-32}[/tex]
[tex]x2=\frac{-1241.25 }{-32}[/tex]
x2= 38.789 ≅ 38.8 seconds
Time cannot be negative. So, the projectile will hit the ground after 38.8 seconds.
HELP PLEASE, NO FILES OR LINKS PLEASE
Thomas is going to deposit $840 in an account that earns 7.5% interest compounded annually. His wife Sheril will deposit $1,250 in an account that earns 6.9% simple interest each year. They deposit the money on the same dayand make no additional deposits or withdrawals for the accounts. What statement is true concerning Thomas' and Sheril's account balance after 5 years?
a
Thomas' account will have about $475.32 less than Sheril's account.
b
Sheril's account will have about $475.32 less than Thomas' account.
c
Thomas' account will have about $431.25 less than Sheril's account.
d
Sheril's account will have about $431.25 less than Thomas' account.
Answer:
A
Step-by-step explanation:
I am to determine the future value of Thomas' deposit with annual compounding
The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = Present value
R = interest rate
N = number of years
840 x (1.075)^5 = 1205.93
I am to determine the future value of Sherill's deposit in 5 years using simple interest
The amount that would be in the account = amount deposited + interest earned on deposit
interest earned on deposit can be determined by determining the simple interest
Simple interest = amount deposited x time x interest rate
1250 x 0.069 x 5 = 431.25
Amount that would be in her account after 5 years = 1250 + 431.25 = 1681.25
Sheril's money is higher by - 1681.25 - 1205.93 = 475.32
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 :)❤
A polygon is shown.
The area of polygon MNOPQR = Area of a rectangle that is 9 square units + Area of a rectangle that is ___ square units.
Answer:
Area of a rectangle that is 9 units² + Area of a rectangle that is 4 units²
Step-by-step explanation:
Line PQ is 1 unit because 3 units - 2 units = 1 unit
Line PO is 4 units because 7 units - 3 units = 4 units
1 unit × 4 units = 4 units²
4 units² + 9 units² = 13 units²
Answer:
adding an answer so the other guy can get brainlist!
Step-by-step explanation:
Could someone please help me...... this is hopeless.....
Answer:
[tex]m=-\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{9-10}{6-4}[/tex]
help help please answer this question and no link
Which exponential equation is equivalent to this logarithmic equation?
log x = 4
Answer:
B
Step-by-step explanation:
Use the definition of a logarithm, log b ( x ) = y ⟹ b y = x , to convert from the logarithmic form to the exponential form. 10^ 4 = x
The exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x
What is logarithm ?When you raise a number with an exponent, there comes a result.
Lets say you get [tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.
Log with base 10 is written as [tex]\log(x)[/tex] simply.
The given logarithmic equation is;
[tex]\log x = 4[/tex]
Since, log with base 10 is written as [tex]\log(x)[/tex] simply, therefore, we have:
[tex]\log_{10} x = 4[/tex]
Using the definition of logarithm, we get;
[tex]x = 10^4[/tex]
Equivalently, [tex]10^4 = x[/tex] (option B).
Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x
Learn more about logarithm here:
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Find the area of the polygon.
2.cm
3 cm
2 cm
Beth has to do 20 math problems tonight. She has completed 20%. How many problems has she completed?
Answer:
She has completed 4 problems
Step-by-step explanation:
Take the total number of problems and multiply by the percent completed
20 * 20%
20 * .20
4
She has completed 4 problems
Answer:
4
Step-by-step explanation:
(a) degree 4, 3 zeros, 3 turning points,
and negative leading coefficient
Step-by-step explanation:
Use this polynomial.
[tex] - x {}^{4} +9x {}^{3 } + 13 {x}^{2} - 45x - 50[/tex]
A degree 4 means our leading coefficient looks like.
[tex] {x}^{4} [/tex]
Since our degree is 4, our turning points would be 3.
Since we have three roots, we need two single roots and a double root.
A negative leading coefficient would have a negative sign in front of it.
Use another site to help graph the actual graph
The Colonel spots a campfire at a bearing N 71 ∘ E from his current position. Sarge, who is positioned 235 feet due east of the Colonel reckons the bearing to the fire to be N 45 ∘ W from his current position. Determine the distance from the campfire to each man, rounded to the nearest foot.
Answer:
[tex]X=85.123m[/tex]
[tex]Y=184.88m[/tex]
Step-by-step explanation:
From the question we are told that:
Campfire Bearing from Colonel[tex]x=N 71 \textdegree E[/tex]
Distance b/w Colonel and Sarge [tex]Z=235feet[/tex]
Campfire Bearing from Sarge [tex]y=N 45 \textdegree E[/tex]
Generally the angles x' and y' are solved
[tex]x'=90 \textdegree-71 \textdegree[/tex]
[tex]x'=19 \textdegree[/tex]
[tex]y'=90 \textdegree-45 \textdegree[/tex]
[tex]y'=45 \textdegree[/tex]
Generally the angle z' is solved
Sum of angles of a triangle is 180
Therefore
[tex]z'=180 \textdegree-(19+45) \textdegree[/tex]
[tex]z'=116 \textdegree[/tex]
Generally the sine rule equation for for all distances is mathematically given by
[tex]\frac{Z}{sinz'}=\frac{X}{sinx'}=\frac{Y}{siny}[/tex]
Generally the the distance b/w the Colonel and the campfire X is mathematically given as
[tex]\frac{235}{sin116}=\frac{X}{sinx'}[/tex]
[tex]\frac{235}{sin116}=\frac{X}{sin19}[/tex]
[tex]X=85.123m[/tex]
Generally the the distance b/w Sarge and the campfire X is mathematically given as
[tex]\frac{235}{sin116}=\frac{Y}{siny}[/tex]
[tex]\frac{235}{sin116}=\frac{Y}{sin45}[/tex]
[tex]Y=184.88m[/tex]
Jessie has successfully made 35 of her last 50 free throw attempts. Based on this information, what is the BEST calculation of the probability that she will make her next free throw?
Answer:
C. 70%
Step-by-step explanation:
35 / 50 = 70/100 = 70%
So she will be 70% accurate in the next shot.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
please help me tysm !!
helpppp me pleaaaaseeeewww
Answer:
A
Step-by-step explanation:
I believe it is A If I remember correctly
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.
learn more about linear equations here :
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hour friends earned more than $400
working at a stack stand. After
paying their parents $50 for
providing supplies, the friends
divided the remaining money equally
among themselves. Which inequality
could the friends have used to find
m, the amount of money each would
receive?
A 4m + 50 > 400
B 4+ 50m < 400
C 50m + 45 400
D 4m + 50 < 400
Answer:
the answer is D :)
Step-by-step explanation:
Write a recursive formula for an, the nth term of the sequence 3, -1, -5, ....
Tn = a + (n-1) d
= 3 + (n-1) (-4)
= 3 -4n +4
= 7-4n
hope it helped you dear
Tyrone is making 52 cookies for a party. Some will be a pecan cookies and some will be honey ginger. The ratio pecans a honey ginger is 76. How many of each kind of cookie will he make
Complete Question
Tyrone is making 52 cookies for a party. Some will be a pecan cookies and some will be honey ginger. The ratio of pecans to a honey ginger is 7:6. How many of each kind of cookie will he make
Answer:
28 pecan cookies and 24 Honey ginger cookies
Step-by-step explanation:
From the above question
Pecans : Honey ginger = 7:6
Sum of Proportion = 7 + 16 = 13
Total number of cookies = 52
Number of pecans
= 7/13 × 52 = 28 pecans cookies
Number of Honey ginger
= 6/13 × 52 = 24 Honey ginger cookies
Therefore, we have:
28 pecan cookies and 24 Honey ginger cookies
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!
ASAP- Solve the system of equations and choose the correct answer from the list of
options. (4 points)
x - y = 7
y = 3x + 12
01 (3
O2)
2) (3)
03 ()
04 (2)
hello please help thanks
Someone please help me ! Im behind on school work and Im trying to improve my grades! <3
Determine if the product of 3/2and 8/18 is rational or irrational. Explain your answer.
Answer:
Step-by-step explanation:
h