The ratio of the area of the smaller square to the area of the larger square, that have a perimeter ratio of 2:7 is 4:49
According to the given question.
The perimeters of two squares are in the ratio 2 : 7
The perimeter of a square of side x is 4x
The comparative length of the side of each square are 2/4 and 7/4
And, the comparative area are
(2/4)² and (7/4)²
Therefore, the ratios of the areas of the area of the smaller square to the area of the larger square
(2/4)² : (7/4)² = 1/4 : 49/16
⇒ 16×1/4 : 16×49/16
⇒ 4:49
Hence, the ratio of the area of the smaller square to the area of the larger square is 4 : 49
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nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.
The given statement is true because it is the definition of nonlinear optimization.
it is the branch of mathematics with deals with the basic mathematical operators called arithmetic operators are addition, division, multiplication and subtraction.
Here,
The nonlinear optimization problem is an optimization problem in which at least one term in the objective function or a constraint is nonlinear, is true, Since its the basic definition of nonlinear optimization.
Thus, the given statement is true.
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Answer the 2 questions in photo [ Brainliest + easy points ]
Answer:
14. 41
15. 4
Step-by-step explanation:
I used Substitution.
2(14)+13 = 41
3(2) - 2 = 4
Answer: EF = 29 units and KM = 22 units
Step-by-step explanation: For the first one, we just add EF and FG, x+14 and 14, and make it equal to EG, 2x+13. We then get x+28 = 2x+13, x = 15. EF = x + 14 and then sub in 15 for x to get 29.
For KM, same deal as the first one. KL and LM, 6 and 2x, equals to KM, 3x-2. 2x+6 = 3x - 2. x = 8. KM = 3x - 2. sub in 8 for x and then we get 22.
3. Use your estimates to find out how many times more massive Jupiter is than
Mercury. Express your answer in standard form (without using a power of 10). Show
your work. (4 points)
Jupiter is 5,751.51 times more massive than Mercury.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The mass of the planet Jupiter is given below.
1,898,000,000,000,000,000,000,000,000 kg.
The scientific notation is:- 2 x 10²⁷ kg.
The mass of the planet Mercury is given below.
330,000,000,000,000,000,000,000 kg.
The scientific notation is:- 3.30 x 10²³ kg.
Divide the mass of the planet Jupiter by the mass of the planet Mercury. Then we have
Jupiter / Mercury = 2 x 10²⁷ / 3.30 x 10²³
Jupiter / Mercury = 5,751.51
Your question was incomplete, but the complete question was given below.
The most massive planet in the solar system, Jupiter, has a mass of about 1,898,000,000,000,000,000,000,000,000 kg.
The least massive planet is Mercury, which has a mass of about 330,000,000,000,000,000,000,000 kg.
Use your estimates to find out how many times more massive Jupiter is than Mercury. Express your answer in standard form (without using a power of 10).
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pls help me solve this question
Answer: 57.75 m or about 57.8m
Step-by-step explanation:
Which number produces a rational number when added to 0.6?
Answer:
D is the answer
Step-by-step explanation:
please make my answer as brainelist
What is the density of a piece of wood with a mass of 25 kg and a volume of 0.0385 m 3
Answer:
≈649 kg/m[tex]^{3}[/tex]
Step-by-step explanation:
Density is equal to mass/volume
25 / 0.385 ≈ 649 kg/m[tex]^{3}[/tex]
Which is faster?
The number of bacteria colonies doubling every 80 minutes
Or
The number of bacteria colonies quadrupling after 4 hours (once?)
Answer:
A. the number of bacteria colonies doubling every 80 minutes.
Step-by-step explanation:
A. 2 cells = 80 mins
B. 4 cells = 80 mins
how to check;
multiply both sides by 2 in equation A
2 × 2 = 80 × 2
4 cells = 160 mins
change the mins into hours
4 cells = 160 ÷ 60
4 cells.= 2 hrs 40 mins
coagulate results
equation A. is 4 cells = 2hrs 40 mins
equation B. is 4 cells = 4 hrs
therefore equation A. is faster
please if found helpful rate brainliest
Help for BRAINLIEST! Find BC
The length of the segment BC is equal to 5√3 π / 3.
What is the length of a missing side of a geometric system?
Herein we find the a geometric system formed by a circle and an inscribed right triangle formed by two right triangles. By a quick inspection we find the following measures:
AD = 10π, m ∠ BCD = 60°, m ∠ BDC = 30°, m ∠ BDA = 60°, m ∠ BAD = 30°
Then, by 30-60-90 right triangle theorem we find that:
DB = (1 / 2) · AD
DB = (1 / 2) · 10π
DB = 5π
DB = √3 · BC
BC = (√3 / 3) · DB
BC = 5√3 π / 3
The length of the segment BC is equal to 5√3 π / 3.
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when $n$ is divided by 10, the remainder is $a$. when $n$ is divided by 13, the remainder is $b$. what is $n$ modulo 130, in terms of $a$ and $b$? (your answer should be in the form $ra sb$, where $r$ and $s$ are replaced by nonnegative integers less than 130.)
[tex]\bold{n\equiv 91a+40b\ mod \ 130}[/tex]
Given that a is the remainder when n is divided by 10. Then, [tex]n\equiv a\ mod 10[/tex]
Also b is the remainder when n is divided by 13 i.e., [tex]n\equiv b\ mod 13[/tex]
Then by Division algorithm, there are integers k and m such that n = a + 10k and n = b + 13m
These two equations are equivalent to
13n = 13a +130k and 10n = 10b + 130m
Adding these two equations, 23n = 13a + 10b + 130(k + m)
⇒ [tex]23n\equiv 13a+10b\ mod\ 130[/tex]
gcd (23,130) = 1
So 23 has an inverse modulo 130.
Therefore, [tex]n\equiv 23^{-1} (13a+10b) \ mod\ 130[/tex]
Applying Euclidean algorithm for 130 and 23,
130 = 23 x 5 + 15
23 = 1 x 15 +8
15 = 1 x 8 +7
8 = 1 x 7 + 1
Therefore, 1 = 8 - 7 = 8 - (15 -8 ) = 2 x 8 - 15 = 2( 23 - 15 ) - 15
= 2 x 23 -3 x 15 = 2(23) -3(130-5x23) =17(23) -3(130)
So inverse of 23 = 17
So, [tex]n\equiv 17 (13a+10b) \ mod\ 130\equiv 221a +170b \ mod \ 130 \equiv \bold{91a+40b \ mod\ 130}[/tex]
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Please help math 30 points
Answer:
298781
Step-by-step explanation:
You borrow $1,300 from a friend and promise to pay back $1,800 in 2 years. What simple interest rate in percent will you pay?
The simple interest rate will be 19.2% per year.
We need to find the simple interest which is I = P * R * T
where,
I is the interest,
P is the principal,
R is the interest rate and
T is the time period.
Here, I = the amount you payed - the amount that you owed
= $1800 - $1300 = $500
Now, I = 500
T = 2 years
P = 1300
According to the formula,
500 = 1300 * R * 2
⇒ 500 = 2600* R
∴R = 500/2600 = 0.1923
Multiplying it by 100, we get 19.23%.
Rounding off 1 decimal place, we get 19.2%.
Therefore, you will pay simple interest rate of 19.2% per year.
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Simplify each expression for x=6 a. 12x^0(x^-4) b. 14(x-2)
After solving the expressions we get the value for each of it as:
a. 1/108
b. 7/18
Given:
a. 12x⁰(x⁻⁴)
Apply the multiplication property of exponents.
when variables multiply, the powers are added.
12x⁰⁻⁴
12x⁻⁴
substitute the value of x = 6 in the above term.
12(6)⁻⁴
12 × 1/6⁴
12 × 1/1296
1/108
b. 14(x⁻²)
The algebraic technique for resolving simultaneous linear equations is called the substitution method. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.
directly substitute the value of the x in the expression.
14(6)⁻²
14 × 1/6²
14 × 1/36
7/18
hence after evaluating expressions we get the values as 1/108 and 7/18.
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judy measured a summer camp and made a scale drawing. the scale she used was 19 centimeters : 8 meters. in the drawing, the sand volleyball court is 38 centimeters long. what is the length of the actual volleyball court?
As per the drawing scale, the actual length is 16m.
What is a drawing scale?
A length at full size: The length at the scale hired this is the identical period is how the size of works is expressed as a ratio. drawing, for example, would be 1:1.A drawing or representation of a authentic aspect that has been scaled up or down out of its original size at the same time as last proportionate to a actual item is called a scale drawing. Scale ratio refers to the share in which a drawing of such an object is shrunk or increased.Given scale is,
19:8
Therefore,
To determine the, actual length,
[tex]\frac{19}{8} =\frac{38}{actual\ length}[/tex]
⇒ actual length = [tex]\frac{38}{19}*8[/tex] = 16m.
Hence, as per the drawing scale the actual length is 16m
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Question
Evaluate.
−26.6
-----------
−1
Enter your answer in the box.
The value of the expression given as −26.6/−1 is 26.6
How to evaluate the expression?The expression is given as
−26.6
-----------
−1
Rewrite the above expression properly as follows
So, we have
−26.6/−1 or −26.6 ÷ −1
This is so because the expression is a quotient expression
So, we have
−26.6/−1
Express −26.6 as -13.3 - 13.3
So, we have the following equation
−26.6/−1 = (−13.3 −13.3)/−1
Expand the expression
So, we have
−26.6/−1 = (−13.3)/−1 + (−13.3)/−1
Evaluate the quotients in the above equation
So, we have
−26.6/−1 = 13.3 + 13.3
Evaluate the quotients in the above equation
So, we have
−26.6/−1 = 26.6
Hence, the value of the expression given as −26.6/−1 is 26.6
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To isolate a single variable when rearranging equations, move all other variables to the.
To isolate a single variable when rearranging equations, move all other variables to the other side of the equation.
According to the statement
We have to find that the rearrangement of the variables.
So, For this purpose, we know that the
A variable is a symbol and placeholder for any mathematical object.
From the given information:
To isolate a single variable when rearranging equations.
Then for this:
To isolate a single variable when rearranging equations,
Then move all other variables to the other side of the equation by using the opposite function on them and remembering to perform that operation on both sides of the equation. Make sure the rearrangement has the target variable in the numerator, not the denominator.
So, To isolate a single variable when rearranging equations, move all other variables to the other side of the equation.
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is it true a cylinder is a polyhedron where two faces are parallel and congruent and the remaining faces are parallelograms
It is "false" that a cylinder is a polyhedron where two faces are parallel and congruent and the remaining faces are parallelograms. Its is a prism.
What is a prism?A polyhedron of two polygonal faces in parallel planes & parallelograms on the other faces is called prism.
Some features regarding the prism are-
A prism is a type of polyhedron with two parallel and congruent faces known as bases, and the other faces were indeed parallelograms. The base is the pair of identical shapes in a prism; there seem to be two bases on a prism that really are congruent and parallel. These bases are N-sided and polygonal. Prisms abound in our surroundings, such as the locker in our bedroom and skyscrapers.Prisms come in a variety of shapes, including Rectangular Prisms, Pentagon shaped Prisms, Triangular Prisms, Pyramids as Prisms, and Hexagonal Prisms. They each are given their own polygon as a base and parallelogram faces.To know more about the prism, here
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write the standard form of a complex number using a for the real part and b for the imaginary coefficient
The standard form the Complex number having real part "a" and imaginary part"b" is a+ib.
Complex number:
Basically, a Complex number is made up of two numbers: a real number and an imaginary number. A+iB, where an is a real number and ib is an imaginary number, is a Complex number. A and B are real numbers.
As a result, a Complex number is just a straightforward way to describe the addition of two integers, a real number and an imaginary number. It is divided into two parts: a pure actual component and a pure fictitious part.
Therefore,The standard form the complex number having real part "a" and imaginary part"b" is a+ib.
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Answer:It’s a+bi
Step-by-step explanation:
The picture has the question.
Answer: 180 tickets for $40
Step-by-step explanation:
To answer this question, we need to find a pattern;
15 / 3 = 5
60 / 15 = 4
-> If you divide, we find a pattern of the quotient with 5... 4... so we can assume the next is 3
Using this pattern;
60 * 3 = 180 tickets for $40
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
Step-by-step explanation: its 32
Answer:
Step-by-step explanation:
A + B + C = 180
A = 47
B = 62
C = ???
We don't know what "C" is??
So..
A + B + C = 180
C = 180 - A - B
C = 180 - 47 - 62
Subtract those numbers and you should get 71
Soo..
C = 71
we can also add up
47 + 62 + 71 = 180
so if you get 180 when you add them up then that's your correct answer!!
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5. Reem paid £62 for a bicycle.
She sold it later for £46.
What was her percentage loss?
Step-by-step explanation:
[tex] \frac{46}{62} \times 100 = 74.19 percent \\ 100 - 74.19 = 25.81 \: percent \\ her \: loss \: was \: 25.81 \: percent[/tex]
find the solution to this equation: 4x-2(x-3)=-7+5x+4
Answer:
x=3
Step-by-step explanation:
4x-2x+6=-7+5x+4
2x+6=-7+5x+4
2x+6-6=5x-3-6
2x=5x-9
-3x=-9
x=3
Remote Interior and Exterior Angles in Triangles
Answer:
∠ 2 = 60°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 remote interior angles.
123° is an exterior angle of the triangle , then
∠ 2 + 63° = 123° ( subtract 63° from both sides )
∠ 2 = 60°
Answer:
60
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180° so we can write the following equation to find the value of missing angle:
∠2 + 63 + 57 = 180 add like terms
∠2 + 120 = 180 subtract 120 from both sides
∠2 = 60
Help me please i cant do this
Answer: Can you give choices that in the problem
Step-by-step explanation:
please simplify! i do not understand, work shown please!
[tex]2xy \sqrt[3]{3y {}^{ \: 2} } [/tex]
Describe the graph of the Celsius-Fahrenheit relationship
Using linear function concepts, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the table, we have that:
When the input is of 0, the output is of 32, hence the intercept is of 32.When the input changes by 10, the output changes by 18, hence the slope is of 18/10 = 1.8.Thus, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.
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A rectangular park is 15 miles long and 5 miles wide. How long is a pedestrian route that runs diagonally across the park?
The pedestrian route that runs diagonally across the park is 5√10 miles.
What is the Pythagorean theorem?It states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
We have,
A rectangle:
Length = 15 miles
Wide = 5 miles
Diagonal length can be considered as the hypotenuse.
Applying the Pythagorean theorem.
Diagonal side² = length² + wide²
Diagonal side² = 15² + 5²
Diagonal side² = 225 + 25 = 250
Diagonal side = √250 = 5√10 miles.
Thus the pedestrian route that runs diagonally across the park is 5√10 miles.
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Toni rows a boat 4.5 km/h upstream and then turns around and rows 5.5 km/h back downstream to her starting point. If her total rowing time is 1.5 h, for how long does she row upstream?
Express your answer to the nearest minute. Make the table, write equations and solve.
Answer:Q
Step-by-step explanation:1+2-3+4=1
Find the distance between the points E(3, 7) and F(6, 5).
Step-by-step explanation:
Therefore, the distance between E ( 3 , 7 ) E(3,7) E(3,7) and F ( 6 , 5 ) F(6,5) F(6,5) is approximately 3.61 \textbf{3.61} 3.61 units.
express the following equation in the form y=mx+c and identify the gradient:
2y=7x-5
5x-3y=4
10-2x+3y=0
Answer:
y = 7/2x - 5/2 ; gradient is 7/2
y = 5/3x - 4/3 ; gradient is 5/3
y = -2/3x - 10/3; gradient is -2/3
Step-by-step explanation:
2y = 7x-5
2y/2 = (7x - 5)/2 y = 7/2x - 5/25x - 3y=4
(5x-3y) -5x = 4 -5x -3y = -5x + 4-3y/-3 = (-5x+4)/-3 y= 5/3x - 4/310 - 2x+3y = 0
(10-2x+3y) -10 = 0 - 10-2x + 3y = -10(-2x + 3y) + 2x = -10 + 2x 3y = 2x -10 3y/3 = (2x - 10)/3 y = 2/3x -10/3NOTE: The gradient is the slope
Johns weekly salary is $478.25. his employer is changing the pay period to semimonthly. What is johns annual salary?
What will johns semimonthly salary be to the nearest cent
Based on the fact that the employer is changing the pay period to semimonthly, John's semimonthly salary to the nearest cent is $956.50
John's annual salary can be found to be $24,869
How to find the semimonthly salary?If a person is paid semimonthly, it means that they are paid twice a month or every two weeks.
This means that John's semimonthly salary is:
= 478.25 x 2
= $956.50
In a year, John's annual salary will be:
= 478.25 x 52 weeks
= $24,869
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