I need help with finding the rational approximation of 37 using perfect squares
Answers
SOLUTION
For rational approximation of 37, it means we are to obtain the close estimate for the square root of 37.
using perfect squares,
The perfect square number immediately lower than 37 is
[tex]36[/tex]The perfect square number immediately higher than 37 is
[tex]49[/tex]Then we set up the problem as in the image below
The distance between 36 to 37 is lower than the distance between 49 to 37, hence the rational aproximation of 37 will be closer to the square root of 36 than the square root of 49.
This accouunt for the sqaure root of 37 in the image above
[tex]\sqrt[]{37}=6.08\approx6.1[/tex]Therefore
The rational aprosimation of 37 using perfect square is 6.1
Related Questions
how can i get an elimination out of this equatio
Answers
The simultaneous equations are:
[tex]\begin{gathered} -2x+7y=-23 \\ 6x-7y=-1 \end{gathered}[/tex]Since, the unknown y has the same co-efficient across the two(2) equations, we can eliminate it directly.
Thus, we have:
[tex]\begin{gathered} -2x+7y=-23 \\ 6x-7y=-1 \\ ----------- \\ -2x+6x=-23-1 \\ 4x=-24 \\ x=\frac{-24}{4} \\ x=-6 \end{gathered}[/tex]To find y, substitute for x = -6 into any of the equations.
Thus, we have:
[tex]\begin{gathered} \text{from equation i)} \\ -2x+7y=-23 \\ -2(-6)+7y=-23 \\ 12+7y=-23 \\ 7y=-23-12 \\ 7y=-35 \\ y=-\frac{35}{7} \\ y=-5 \end{gathered}[/tex]Hence, the correct option is option A
Frank uses 27/5 tablespoons of pista extract to make 9 servings of a recipe. How many tablespoons of pista extract does each serving need?
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Answer: 3/5 tablespoons.
You are making a kite and need to figure out how much binding to buy. You need the binding for the perimeter of the kite. The binding comes
in packages of two yards. How many packages should you buy?
12 in.
15 in.
12 in.
20 in.
You should buy packages.
Answers
With the help of the Pythagorean theorem, we know that we should buy 3 packages.
What is the Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.So, Pythagorean formula: c² = a² + b²
Each package contains 2 yards of binding.In the kite, there are right triangles, so use the Pythagorean theorem.(Refer to the image of the kite attached below)
△1:
a² + b² = c²15² + 12² = x₁²x₁ = √15² + 12²x₁ = 19.2 in△2:
x₂ = x₁ = 19.2 in
△3:
a² + b² = c²12² + 20² = x₃²x₃ = √12² + 20²x₁ = 23.3 in△4:
x₄ = x₃ = 23.3 inTotal: 19.2(2) + 15 + 2(12) + 20 + 2(23.3) = 144 in
Total (actual) > 144 inNow,
1 package = 2 yards = 6ft = 72 in2 yards × 3ft/1yrd × 12in/1ft = 72 in2 packages: 2(72) = 144 in3 packages: 3(72) > 144So, we should buy 3 packages.
Therefore, with the help of the Pythagorean theorem, we know that we should buy 3 packages.
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X 즈 - + 3 = 15 -4someone help me confused
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First we have to transfer the number 3 the other side of equal sign as follows,
[tex]\begin{gathered} \frac{x}{-4}=15-3 \\ \frac{x}{-4}=12 \end{gathered}[/tex]Now, we need to transfer (-4) to the other side of the equal side by multiplying with the number 12.
[tex]\begin{gathered} \frac{x}{-4}=12 \\ x=12\ast(-4) \\ x=-48 \end{gathered}[/tex]Thus, the answer of the x is (-48).
A triangle has angle measurements of 15°, 90°, and 75°. What kind of triangle is it?
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The triangle has one angle of 90 degrees, so it is a rigth triangle.
As the other two angles are different between them, the triangle is also scalene (all sides are different)
.
64, 57, 50, 43, ... 50th term
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For the next series, we will calculate its expression
[tex]v(n)=64-7(n-1)[/tex]For n = 1
v = 64
For n = 2
v = 57
For n = 3
v = 50
For n = 50
v = -279
helppppppppppppppppppppppppppppppp
Answers
Answer:
b=4
I believe this is correct.
Step-by-step explanation:
-(2)^3+7(2)^2-2(2)+12=
-8+28-16
-8+12
4
ABC is a right angle. What is the measusre of DBE?
Answers
According to the given diagram the sum of ABD, DBE and EBC must be 90. Use this information to find the measure of DBE:
[tex]\begin{gathered} 33+\measuredangle DBE+33=90 \\ \measuredangle DBE=90-33-33 \\ \measuredangle DBE=24 \end{gathered}[/tex]The measure of DBE is 24 degrees.
U.S. Customary unit conversion with mixed number values: One...Charlie bought 5 feet of fabric. How much is this in yards?Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.0OlaDOinftyd목x 5?Please help
Answers
Converting feet into yards.
Recall that one yard =3 feet
[tex]1\text{ yard=3 f}eet[/tex]Multiply by 5/3 on both sides, we get
[tex]1\times\frac{5}{3}\text{ yard=3 }\times\frac{5}{3}\text{f}eet[/tex][tex]\frac{5}{3}\text{ yard=}5\text{f}eet[/tex][tex]\text{Use }\frac{5}{3}=1\frac{2}{3}[/tex][tex]1\frac{2}{3}\text{ yard=}5\text{f}eet[/tex]The answer is
[tex]1\frac{2}{3}\text{ yards}[/tex]If the radius of a sphere increases from 3 feet to 9 feet, by how many cubic feet does the volume of the sphere increase? 967 ft3 A 1087 ft3 936 ft 0
Answers
The volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]The original sphere, with radius r=3, has volume:
[tex]\begin{gathered} V=\frac{4}{3}\pi(3)^3 \\ =36\pi \end{gathered}[/tex]The second sphere, with radius r=9, has volume:
[tex]\begin{gathered} V=\frac{4}{3}\pi(9)^3 \\ =972\pi \end{gathered}[/tex]To find how much the volume increased we substract the first volume to the second one:
[tex]972\pi-36\pi=936\pi[/tex]Therefore the v
in a bag there are red and green balls in the ratio of 2:7. if there are 14 red balls,how many green balls are there
Answers
For the information given in the statement you have
[tex]\frac{\text{ number of red balls}}{\text{ number of green balls}}=\frac{2}{7}[/tex]Then
[tex]\frac{2}{7}=\frac{14\text{ red balls}}{x\text{ green balls}}[/tex]Solving for x
[tex]\begin{gathered} \frac{2}{7}=\frac{14}{x} \\ \text{ Apply cross multiplication} \\ 2\cdot x=14\cdot7 \\ 2x=98 \\ \text{ Divide by 2 into both sides of the equation} \\ 2x=\frac{98}{2} \\ x=49 \end{gathered}[/tex]Therefore, there are 49 green balls.
Lindsay is designing a dog pen. The original floor plan is represented by figure PQRS. Lindsay dilates the floor plan by a scale factor of 1/2 with a center of dilation at the origin to form figure P'Q'R'S'. The final figure is P"Q"R"S". What are the coordinates of P'Q'R'S'?
Answers
Since we have the original coordinates P(-6, 9), Q(3, 9), R(3, 3) & S(-6, 3) and the scale factor, we multiply each x-component and y-component of each point by 1/2 in order to get P'Q'R'S', that is:
P'(-3, 9/2)
Q'(3/2, 9/2)
R'(3/2, 3/2)
S'(-3, 3/2)
And those are our P'Q'R'S' coordinates after the scaling,
I need help on a part of very hard question cuz it isn't very very very very very very far oh yeah. hear it is 2+2
Answers
Given:
The objective is to find the solution of 2+2.
Since the required operation in the given question is addition.
So, the addition of 2 and 2 will be,
[tex]2+2=4[/tex]Hence, the answer is 4.
A circle has a circumference of 43.96 inches. What is the area?
Answers
Solution:
Given that the circumference of the circle is
[tex]C=43.96in[/tex]Step 1:
Calculate the radius of the circle
To calculate the radius of the circle, we will use the formula below
[tex]\begin{gathered} C=2\pi r \\ \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} C=2\pi r \\ 43.96=2\times\pi\times r \\ 43.96=6.28r \\ \text{divide both sides by 6.28} \\ \frac{6.28r}{6.28}=\frac{43.96}{6.28} \\ r=7in \end{gathered}[/tex]Step 2:
Calculate the area of the circle using the formula below
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where,} \\ \pi \\ r=7in \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi\times7^2 \\ A=\pi\times49 \\ A=153.94in^2 \end{gathered}[/tex]Hence,
The Area of the circle is = 153.94 in²
10. A recipe for banana bread calls for 3 bananas for every 6 cups of
What is the ratio of bananas to sugar?
Answers
1:2
Explanation:
If we divide both terms in the ratio 3:6 by the number 3, it equals 1:2
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Explain why (-1)^n = 1 for any even number n.How is this possible? I thought it would equal -1. Does that mean the answer is "not possible"?
Answers
The expression (-1)^n means the number -1 multiplies itself n times.
So for example if n = 2, we have that:
[tex](-1)^2=(-1)\cdot(-1)=1[/tex]For n = 3, we have:
[tex](-1)^3=(-1)\cdot(-1)\cdot(-1)=1\cdot(-1)=-1[/tex]For n = 4:
[tex](-1)^4=(-1)^2\cdot(-1)^2=1\cdot1=1[/tex]We can see that the result alternates from -1 and 1, and when n is odd, the result is -1, and when n is even, the result is 1.
So for any even number n, the result will be 1.
Is the point (-2, 2) a solution for the equation y-4 = 3(x + 1)?
Answers
Remember that ordered pairs are written in the form:
[tex](x,y)[/tex]To find it (-2,2) is a solution for the given equation, substitute x=-2 and y=2:
[tex]\begin{gathered} y-4=3(x+1) \\ \Rightarrow2-4=3(-2+1) \\ \Rightarrow-2=3(-1) \\ \Rightarrow-2=-3 \end{gathered}[/tex]Since the expression -2=-3 is false, then the point (-2,2) is not a solution for the given equation.
Colton’s gym charges an initiation fee of $40 plus a monthly fee of $50 . Which of the following he equations below shows the cost c of joining the gym for m months ? A . C = 50 + 40mB . C = 40 + 50mC. C = 40 - 50 m
Answers
given that Colton gym charges initial fee of $40
there is an addiontional fee of $50
C is the cost of joining the gym
m is the number of months
so the equation that can show the cost of joining the gym in m month is:
$40 which is the initial feel been added to $50 the additional charge multiply by m the number of months.
therefore the equation is:
C = 40 + 50m
so the correct option is B
Julie has a total of 16 chickens. If she has 4 times as many chickens as dogs, write and solve an equation to determine the number of dogs she has.
Answers
The equation that can be used to determine the number of dogs that Julie has =
4× (number of chicken) = 64
What is an equation?An equation is defined as the expression that shows a connection between two variables that are connected with an 'equal to' sign.
The number of chicken owned by Julie = 16 chickens
The number of dogs = X
But she has 4× (number of chicken) = X
That is 4 × 16 = X
X= 64
Therefore the number of dogs that Julie has = 64 dogs.
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What is the inverse of the given relation?y = 3x + 12I need to understand the step by step breakdown for how to solve this problem.
Answers
Given the function y, we want to find the inverse function y^-1.
Then, replace every x with a y and every y with an x. It yields,
[tex]x=3y+12[/tex]now, solve the equation for y. So, by subtracting 12 to both sides, we have
[tex]x-12=3y[/tex]or equivalently,
[tex]3y=x-12[/tex]and, by dividing both sides by 3, we obtain
[tex]y=\frac{x-12}{3}[/tex]Finally, replace y with y^-1. Then, the inverse function is given by:
[tex]y^{-1}=\frac{x-12}{3}[/tex]vuvvvvvvvyvhvhccvccv
Answers
There are two families who visit a park and pay the entrance fee. The distribution of each family and the total cost paid at the entrance by each are given:
Family 1:
[tex]\begin{gathered} NumberofAdults(A_1\text{ )= 2} \\ NumberofChildren(B_{1\text{ }})\text{ = 3} \\ TotalEntryCost(C_1)\text{= }20\text{ pounds} \end{gathered}[/tex]Family 2:
[tex]\begin{gathered} NumberofAdults(A_2\text{ ) = 1} \\ NumberofChildren(B_2\text{ )= 4} \\ TotalEntryCost(C_2\text{ )= 15 pounds} \end{gathered}[/tex]Now we will define the ticket rates for adults and children at this park:
[tex]\begin{gathered} \text{Adult Rate = x} \\ \text{Children Rate = y} \end{gathered}[/tex]Next step is to express the total entry cost born by each family. This is done by multiplying the rate of each age group with the respective distribution of age group comprising each family.
Family 1:
[tex]\begin{gathered} C_1\text{ = x}\cdot A_1\text{ + y}\cdot B_1 \\ 20\text{ = 2}x\text{ + 3}y\text{ }\ldots.\text{ Eq1} \end{gathered}[/tex]Family 2:
[tex]\begin{gathered} C_2\text{ = x}\cdot A_2\text{ + y}\cdot B_2 \\ 15\text{ = x + 4y }\ldots Eq\text{ 2} \end{gathered}[/tex]We have two equation with two unknowns representing the cost charged for adults ( x ) and cost charged for children ( y ) at the park entrance.
We will solve the equation simultaneously ( Eq1 and Eq2 ) by using the process of Elimination:
[tex]\begin{gathered} 20\text{ = 2x + 3y} \\ -2\cdot(15\text{ = x + 4y) = -30 = -2x -8y} \end{gathered}[/tex][tex]\begin{gathered} 20\text{ = 2x + 3y} \\ -30\text{ = -2x -8y} \\ ========== \\ -10\text{ = 0 -5y} \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = 2}} \end{gathered}[/tex]Plug the value of ( y ) in either of the two equations and solve for ( x ):
[tex]\begin{gathered} 15\text{ = x + 4(2)} \\ x\text{ = 15 - 8} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 7 }} \end{gathered}[/tex]Therefore, the rates charged for each age group are:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{Adult ticket = x = 7 pounds}} \\ \text{\textcolor{#FF7968}{Child ticket = y = 2 pounds}} \end{gathered}[/tex]Answer:yes
Step-by-step explanation:
University DataReceiving Not ReceivingFinancial Aid Financial AidTotalUndergraduates422238988120Graduates18797312610Total6101462910730If a student is selected at random, what is theprobability that the student receives aid and is agraduate (rounded to the nearest percent)? [? ]%
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question 1 A new streaming company charges a rate of $5.99 per month. in order to generate some additional revenue upfront the company is offering a VIP rate of only $3.49 Per month to any subscriber who purchases a VIP pass for one time fee of $21 set up in solving any qualities to determine how many months it would take for subscriber to save money by purchasing the VIP pass
Answers
21 + 3.49x < 5.99x
x > 8.4
Explanations:The normal monthly rate = $5.99
The VIP monthly rate = $3.49
The one time VIP fee = $21
Let the number of months be x
At normal rate, the total charge for x months = 5.99x
For the VIP:
The total charge for x months = 21 + 3.49x
For a subscriber to save money by purchasing the VIP pass, it means the total charge for the VIP must be less than the total charge for the normal subscribers5.99x
Therefore, the inequality to determine how many months it will take for a subscriber to save money by purchasing the VIP pass is:
21 + 3.49x < 5.99x
Solve the inequality above:
21 < 5.99x - 3.49x
21 < 2.5x
2.5x > 21
x > 21/2.5
x > 8.4
Therefore, for a subscriber to save money by purchasing the VIP pass, it would take more than 8.4 months
Can you please help me to answer the question #46
Answers
Part A
S(0) = 1116 - 4.04(0) (Replacing h=0)
S(0)= 1116 (Multiplying)
The answer is 1116 ft/s
Part B
S(10) = 1116 - 4.04(10) (Replacing h=10)
S(10) = 1116 - 40.4 (Multiplying)
S(10)= 1075.06
The answer is 1075.06 ft/s
Part C
S(30) = 1116 - 4.04(30) (Replacing h=30)
S(30) = 1116 - 121.1 (Multiplying)
S(30)= 994.9 (Subtracting)
The answer is 994.9 ft/s.
B 961 m Solve the triangle 40° 41 С b B= degrees minutes m (Round to the nearest whole number.) b = m (Round to the nearest whole number.)
Answers
To find the angle B we can use the propertie that sya that the sum of the internal angles of a triangle is equal to 180º so:
[tex]\measuredangle b+90º+40º,41^{\prime}=180[/tex]and we solve for angle b so:
[tex]\begin{gathered} \measuredangle b=180º-90º-40º,41^{\prime} \\ \measuredangle b=49º,19^{\prime} \end{gathered}[/tex]So B is equal to: 49 degrees and 19 minutes
So now to find a we can use the trigonometric identitie of sin so:
[tex]\begin{gathered} \sin (40.68)=\frac{a}{961} \\ a=961\cdot\sin (40.68) \\ a\approx626 \end{gathered}[/tex]and to find b we use the trigonometryc identitie of cos so:
[tex]\begin{gathered} \cos (40.68)=\frac{b}{961} \\ b=961\cdot\cos (40.68) \\ b\approx729 \end{gathered}[/tex]46) The hundreds digit of the smallest six-digit number divisible by 12, 13,
14, 15 and 16 is
Answers
Answer: 2
Step-by-step explanation:
[tex]12=2^2 \times 3\\\\13=13\\\\14=2 \times 7\\\\15=3 \times 5\\\\16 =2^4\\\\\therefore \lcm(12, 13, 14, 15, 16)=2^4 \times 3 \times 5 \times 7 \times 13=21840[/tex]
Multiplying this by 5 to make it the smallest possible six-digit number, we get 109200, meaning the hundreds digit is 2.
The product 8 and the square of a number decreased by 5 is 67. Find the number.
Answers
Answer:
3 or -3
Explanation:
Let's call the unknown number x. The square of this number is x². The product of 8 and the square of this number is 8x². Finally, it is decreased by 5, so 8x² - 5 and it is equal to 67, then the equation that represents the statement is:
8x² - 5 = 67
Now, we can solve the equation for x. Add 5 to both sides
8x² - 5 + 5 = 67 + 5
8x² = 72
Divide both sides by 8
8x²/8 = 72/8
x² = 9
Find the square root of both sides
x = √9
x = 3 or x = -3
Therefore, the number is 3 or -3
Debra the trainer has two solo workout plans that she offers her clients: plan A and plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did plan A and 3 who did plan B. On Thursday there were 7 clients who did plan A and 9 who did plan B. Debra trained her Wednesday clients for a total of 6 hours and her Thursday clients for a total of 12 hours. How long does each of the workout plans last?
Answers
The solo plans Debra offers her clients are plan A and plan B. Each client can only do one plan .
According to the question the plan only ran on wednesday and thursday.
Wednesday = plan A has 5 client and plan B has 3 clients.
Thursday = plan A has 7 client and plan B has 9 clients.
On wednesday she trained her client for 6 hours.
On thursday she trained her client for 12 hours.
let
x = hour of plan A workout for each client
y = hour of plan B workout for each client
[tex]\begin{gathered} 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}\mathrm{}(i) \\ 7x\text{ + 9y = 12}\ldots\ldots\ldots\text{.(2)} \\ 3y\text{ = 6 - 5x} \\ y\text{ = }\frac{6}{3}\text{ - }\frac{5}{3}x \\ y\text{ = 2 - }\frac{5}{3}x \\ 7x\text{ + 9(2 - }\frac{5}{3}x\text{) = 12} \\ 7x\text{ + 18 - }\frac{45}{3}x\text{ = 12} \\ 7x\text{ + 18 - }15x\text{ = 12} \\ -8x\text{ = 12 - 18} \\ -8x\text{ = - 6} \\ x\text{ = }\frac{6}{8} \\ x\text{ = }\frac{3}{4} \\ 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}(i) \\ 5(\frac{3}{4})\text{ + 3y = 6} \\ \frac{15}{4}\text{ + 3y = 6} \\ 3y\text{ = 6 - }\frac{15}{4} \\ 3y\text{ = }\frac{24-15}{4} \\ 3y\text{ = }\frac{9}{4} \\ y\text{ = }\frac{9}{4}\text{ }\times\text{ }\frac{1}{3} \\ y\text{ = }\frac{9}{12} \\ y\text{ = }\frac{3}{4} \end{gathered}[/tex]on wednesday plan A lasted for 5 * 3/4 = 15/4 hrs and plan B lasted for 3 * 3/4 = 9/4 hrs
On thursday plan A lasted for 7* 3/4 = 21/4 hrs and plan B lasted for 9 * 3/4 = 27/4 hrs
Each of the work out lasted for 3/4 hrs = 0.75 hrs
1) Circle the tables that represent y as a function of x.хХ-31X-10у-5515-3y3608-2-4- 1-2-2-5- 1290у-1-1- 1-11-2-52-5
Answers
The answer is the last table
The answer is the last table
4. A bookstore owner ordered 4032 books. The books were sent in 9 boxes. Each box hadthe same number of books. How many books were in each box?
Answers
448 books in each box
Number of books: 4032
Number of boxes: 9
Since each box had the same number of books, divide the number of books by the number of boxes.
4032/9 = 448