The circumference of ®B is 36 units.
What is scale factor?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
Now it is given that,
The scale factor from ®A to ®B = 1/3
⇒Ks = 1/3
∵ Ks = A/B
By comparison we get,
A = 1
and B = 3
Thus, circumference (CA) of ®A = 12
⇒ Since scale factor for A = 1
⇒ 2πr = 12
⇒ r = 6/π
Now, circumference (CB) of ®B = 2πr = 2π* 6/π
⇒ circumference (CB) of ®B = 12
Since scale factor for B = 3
⇒ circumference (CB) of ®B = 3 * 12
⇒ circumference (CB) of ®B = 36 units.
Thus, the circumference of ®B is 36 units.
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Example 4 PH00F Write a two-column proof of Theorem 4.3 .
The proof of Theorem 4.3 with an example is shown.
What is theorem 4.3?Third Angles Theorem: If two angles of one triangle are congruent with two angles of another triangle, then the third angles must be congruent as well.To prove Theorem 4.3:
Let,s take two triangles, that is △ABC and △ADC.
In which AC⊥BD so ∠ACB ≅∠ACD.As, AC bisects ∠A so, ∠BAC ≅ ∠DAC.Since two pairs of angles are congruent, then the △ABC≅△ADC is under AA condition.
Then, ∠B≅∠D under CPCT condition (corresponding parts of congruent triangles).Therefore, the proof of Theorem 4.3 with an example is shown.
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Write a quadratic equation that passes through the points -2,8 1,14 0,10
By solving a system of equations we can see that the quadratic equation is:
y = x^2 + 3x + 10
How to write a quadratic equation that passes through the given points?
A general quadratic equation is given by:
y = a*x^2 + b*x + c
We want this quadratic equation to pase through the points (-2, 8), (1, 14), and (0, 10).
using the last point, we know that when x = 0, we must have y = 10, then:
10 = a*0^2 + b*0 + c
10 = c
So our quadratic equation is:
y = a*x^2 + b*x + 10
Now we use the other two points to write a system of equations:
8 = a*(-2)^2 + b*(-2) + 10
14 = a*(1)^2 + b*1 + 10
If we simplify these, we get:
-2 = 4*a - 2b
4 = a + b
Isolating a in the second equation we get:
a = 4 - b
Now we replace that in the other equation:
-2 = 4*(4 - b) - 2b
-2 = 16 - 4b -2b
-2 - 16 = -6b
-18/-6 = b = 3
Now that we know the value of b, we replace it in the equation for a:
a = 4 - b = 4 - 3 = 1
Then the quadratic equation is:
y = x^2 + 3x + 10
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a. Which property does the equation 3(g+h)+2 g=(3 g+3 h)+2 g illustrate?
Which property does the equation 3(g+h)+2 g=(3 g+3 h)+2 g illustrate?
Distributive property .
What is distributive property?
According to the distributive property, an expression of the form A(B + C) can be resolved as A (B + C) = AB + AC.Subtraction is similarly subject to this distributive law. This indicates that the distribution of operand A among the other two operands.When we need to multiply a number by the sum of two numbers, the distributive property of multiplication over addition comes into play. In this case, 9(5+5)=9(5)+9(5)=90.To learn more about distributive property, refer:
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A square park has a diagonal walkway from one, corner to another. If the walkway is 120 meters long, what is the approximate length of each side of the park?
F 60 m
G 85 m
H 170 m
J 240m
The approximate length of each side of the park is 85m .
Pythagoras Theorem states that the sum square of two sides of triangle is equal to the square of longest side.
According to the question
given that the park is a square
and in square the longest side is it's diagonal and the diagonal is given to be 120m.
In square all sides of square is same .
let the side be x.
By Applying Pythagoras Theorem in the given ΔABC
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
Substituting the values we get
[tex]x^{2} +x^{2} =120^{2}[/tex]
[tex]2x^{2} =120^{2} \\ \\ 2x^{2} =14400\\ \\ x^{2} =7200[/tex]
[tex]x=\sqrt{7200} =60\sqrt{2}[/tex] = 84.85 ≅ 85
Therefore , the approximate length of each side of the park is 85m .
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[ Brainliest + 20 points]
The smallest angle by which a regular 30-sided figure can be rotated to look exactly like the original figure is __ degrees.
Answer:
12°
Step-by-step explanation:
The angles of the shape should all add to 360°.
We divide this by 30, because the shape has 30 angles.
360° ÷ 30 = 12°.
This is the measure of each angle, and also the degree of rotation. The shape will look like the original figure each time it is rotated 12°.
4 \large \frac{7}{12} + 2 \large \frac{3}{4} + 7 \large \frac{5}{12}
The value of expression [tex]4\frac{7}{12} +2 \frac{3}{4} + 7\frac{5}{12}[/tex] is [tex]\frac{157}{12}[/tex].
We solve this type of fraction by firstly simplifying it into proper fraction. For simplifying it into proper fraction, we multiply denominator of the complex fraction with whole number given with fraction and then add the numerator of the complex fraction
e.g. [tex]4\frac{7}{12}[/tex] = [tex]\frac{12*4+7}{12}[/tex]
so, The given question can be written down as [tex]4\frac{7}{12} +2 \frac{3}{4} + 7\frac{5}{12}[/tex]
i.e. [tex]\frac{35}{12} +\frac{11}{4} + \frac{89}{12}[/tex]
Taking LCM and then writing the equation again
[tex]\frac{35+33+89}{12}[/tex]= [tex]\frac{157}{12}[/tex]
Final answer, the simplified value will be [tex]\frac{157}{12}[/tex]
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Write each subtraction equation as an addition equation.
a - 9 = 6
p - 20 = -30
z - (-12) = 15
x - (-7) = -10
Each subtraction equation as an addition equation is mathematically given as
a - 9 = 6 ==> a=6+9
p - 20 = -30==> p+30=20
z - (-12) = 15 ==> z+12=15
x - (-7) = -10 ==> x+17=0
This is further explained below.
What is the addition equation.?Generally, In mathematics, the summation is the process of adding together a string of any form of numbers, which are referred to as operands or summands; the result is the sum or total of the figures.
In conclusion,
a - 9 = 6 ==> a=6+9
p - 20 = -30==> p+30=20
z - (-12) = 15 ==> z+12=15
x - (-7) = -10 ==> x+17=0
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To determine the number of trout in a lake , a conservationist catches 171 trout,tags them and throws them back into the lake. Later 52 trout are caught; 13 of them are tagged. how many trout would the conservationist expect to be in the lake?
We can expect there to be 684 trout in the lake.
In the given statement is:
To determine the number of trout in a lake, a conservationist catches 171 trout, tags them and throws them back into the lake. Later 52 trout are caught; 13 of them are tagged.
Proportion:
A ratio gives us the measure of one quantity as compared to another quantity, and it is represented either as a fraction, decimal or a notation like a : b. When the same ratio is applicable to other quantities.
Now, According to the question:
Number of trout / number of trout = number of trout caught / caught that were tagged
Number of trout / 171 = 52/13
Number of trout = (171 x 52) / 13
Number of trout = 8,892 / 13 = 684
Hence, We can expect there to be 684 trout in the lake.
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Determine whether each sequence is arithmetic. If so, identify the common difference. 1,3,9,27, . . . .
The given sequence is not arithmetic as the difference of each consequent term with the previous term is not the same.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.Given: 1, 3, 9, 27, ...
Here, 3 - 1 ≠ 9 - 3 ≠ 27 - 9
Since the sequence does not follow the definition of an arithmetic progression, it is not one.
Hence, The given sequence is not arithmetic as the difference of each consequent term with the previous term is not the same.
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A die is rolled. Find the probability of rolling a number greater than 4 .
F. 0.17
G. 0.33
H. 0.5
J. 0.67
The probability of getting a number that is greater than four is G. 0.33
Probability:
Probability defines the possible occurrence of the selected event across the total number of events.
Given,
A die is rolled.
And we need to find the probability of rolling a number greater than 4.
If you roll a single die there are 6 possible outcomes are
=> {1,2,3,4,5,6}
So, the numbers that are greater than 4 are,
=> 5 and 6.
So, there are 2 of which are greater than 4.
So in a single roll the probability of getting a number greater than 4 is
=> 2/6
=> 1/3.
For the decimal form it can be written as,
=> 0.33.
So, the correct option is G. 0.33.
Therefore, the probability of getting the number greater than 4 is 0.33.
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Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. 4,16,64,256,1024, ......
The nth term of seuence is 4^n and the formula for finding the nth term of the given sequence is [tex]a_{n} = 4^{n}[/tex] .
According to the given question.
We have a sequence 4, 16, 64, 256, 1024...
As we know that, a sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.
Here,
The first term of the given sequence is 4, or we can say that 4^1 is 4.
The second term of the sequence is 16, or we can say that 4^2 is 16.
The third term of the sequence is 64, or we can say that 4^3 is 64.
The fourth term of teh sequence is 256, or we can say that 4^4 is 256.
So, if we follow the same pattern or the rule we can say that the nth term of the given sequence is 4^n.
Thereofre, the formula for finding the nth term of the given sequence 4,16,64,256,1024, ...... is [tex]a_{n} = 4^{n}[/tex] where n = 1, 2, 3 , 4....
Hence, the nth term of seuence is 4^n and the formula for finding the nth term of the given sequence is [tex]a_{n} = 4^{n}[/tex] .
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Round the decimal to the nearest whole number. 65.618
Answer:
66
Step-by-step explanation:
The common sparrow has a wingspan of 9 to 15 centimeters. Which inequality matches the wingspan of the common sparrow?
An inequality that matches the wingspan of the common sparrow is 9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.
In this question, we have been given a statement 'The common sparrow has a wingspan of 9 to 15 centimeters. '
We need to write an inequality that matches the wingspan of the common sparrow.
Let x represents the wingspan of the common sparrow.
According to given statement, the common sparrow has a wingspan of 9 to 15 centimeters.
So, the required inequality would be,
9 ≤ x ≤ 15
Therefore, an inequality that matches the wingspan of the common sparrow is 9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.
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Simplify each complex fraction. 1 + 2/x / 2 + 3 / 2x
The Simplified value of the complex fraction 1 + 2/x / 2 + 3 / 2x is (4x+7)/(4x+3) .
A complex fraction is defined as an expression that has fraction in it's numerator and a fraction in its denominator.
For Example : [tex]\frac{\frac{2}{3} }{\frac{5}{7} }[/tex] is an example of complex fraction.
The given question is
=1 + 2/x / 2 + 3 / 2x
[tex]=1+\frac{\frac{2}{x} }{2+\frac{3}{2x} }[/tex]
Taking LCM in the denominator and solving further,
[tex]=1+\frac{\frac{2}{x} }{\frac{4x+3}{2x} }[/tex]
[tex]=1+\frac{2}{x} *\frac{2x}{4x+3}[/tex]
Cancelling out "x" from both numerator and denominator
we get,
=1+(2*2)/(4x+3)
=1+(4)/(4x+3)
Taking LCM as 4x+3 and solving further we get,
=(4x+3+4)/(4x+3)
=(4x+7)/(4x+3)
Therefore , the simplified value of the expression 1 + 2/x / 2 + 3 / 2x is (4x+7)/(4x+3).
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Write an equation of a parabola with vertex at the origin and the given focus.
focus at (6,0)
The equation of the parabola that has vertex at the center and focus at the point (6,0) is x = y²/24
We define what a parabola is
What is a parabola?The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.
The canonical equation of a parabola is given by
(y - k)² = 4p(x - h)
The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.
Since the vertex and the focal axis are on the same axis, we analyze that:
v (0, 0)
f (6, 0) the focus is on the right so the parabola is of the form X = Y².
(y - 0)² = 4p(x - 0)
f = (0 + p, 0)
0 + p = 6
p = 0 + 6
p= 6
(y - 0)² = 4*6(x - 0)
(Y)² = 24(X)
x = y²/24
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State the property that justifies the following statement.
5(3 x+1)=15 x+5
The property that justifies the following statement, 5(3 x+1)=15 x+5 is the distributive property.
Distributive property can be described as one of the properties of multiplication which states that if we multiply two or more values that are added together with a number then the result will be the same even if we multiply each value separately with that number and then add them together. This can be given as:
x(y + z) = xy + xz
Therefore, as 5 x 3 = 15 and 5 x 1 =5, we can write the equation 5(3x+1) as 15x + 5 as the result will be the same in both circumstances.
The distributive property not only justifies the equations when two or more values are added but also justifies the equations in which they are subtracted which can be given as:
x(y-z) = xy - xz
So, according to the distributive property, the statement, 5(3 x+1)=15 x+5 is valid.
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61.3% as a fraction pls
Answer:
[tex]\frac{613}{1000}[/tex]
Step-by-step explanation:
A supermarket wants to find the percent of shoppers who use coupons. A manager interviews every shopper entering the greeting card aisle.
When the supermarket wants to find the percent of shoppers who use coupons. A manager interviews every shopper entering the greeting card aisle. This is a convenience sampling.
What is a convenience sampling?A non-probability sampling technique called convenience sampling includes taking a sample from the nearest area of the population. Pilot testing benefits the most from this kind of sample. The most popular kind of convenience sampling concentrates on gathering data from individuals (the sample) who are 'convenient' for the researcher to reach.
Convenience sampling techniques include inviting friends to take part in your study, gathering information from local sites, mailing surveys, and posting links on social media.
In conclusion, the correct option is A.
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A supermarket wants to find the percent of shoppers who use coupons. A manager interviews every shopper entering the greeting card aisle.
convenience sample
Self-selected sample
systematic sample
random sample
(9.8)²-10² please help
Answer:
Step-by-step explanation:
-9
If <3 measures 123°, what is the measure of <4?
The value of angle 4 is 57°
How to determine the angle
From the image shown, we can see that angle 3 and angle 4 are on a straight line.
It is important to note that angles on a straight line sum up to 180 degrees.
We have angles 1 and 2 are supplementary, that is, they sum up to 180 degrees
Angles 3 and 4 are also supplementary and sum up to 180 degrees
Angles 5 and 6 are also supplementary.
Then, if angle 3 = 123 , we have;
angle 3 + angles 4 = 180
123 + angle 4 = 180
Angle 4 = 180 - 123
Angle 4 = 57°
Thus, the value of angle 4 is 57°
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Given p(x)=−3(x−4)2+14, what is the value of p(2)?
Answer:26
Step-by-step explanation:
-3(2-4)2+14= -3*-2*2+14=12+14=26
Fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.Kyle and his family are planning a vacation in Cancun, Mexico. Kyle wants to convert 200 US dollars to Mexican pesos for spending money. If 278 Mexican pesos are equivalent to 25 , how many pesos will Kyle get for 200?
F. 2178
G. 2224
H. 2396
J. 2504
Converting Mexican pesos to US dollars, Kyle will get 2224 Mexican pesos for 200 US dollars.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
If 278 Mexican pesos is equivalent to 25 US dollars,
278 Mexican pesos = 25 US dollars
Dividing both sides by 25,
278/25 Mexican pesos = 25/25 US dollars
11.12 Mexican pesos = 1 US dollar
Therefore, 1 US dollar is equivalent to 11.12 Mexican pesos.
The conversion factor is 11.12 Mexican pesos/1 US dollar.
If Kyle wants to convert 200 US dollars to Mexican pesos for spending money, and 1 US dollar is equivalent to 11.12 Mexican pesos, multiply the amount by the conversion factor.
200 US dollars (11.12 Mexican pesos/1 US dollar)
= 2224 Mexican pesos
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50pts to whoever can solve these literal equations correctly.
please hurry!!!
Answer:
I'll go with the last option. c=√Em
Find the distance between each pair of points. Round to the nearest tenth. A(1,5) and B(-2,-3)
The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth.
How to find the distance between two points?Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
The distance between two points (x₁, y₁) and (x₂, y₂) is given by ;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
So,
Distance between A(1,5) and B(-2,-3)
[tex]d = \sqrt {\left( {1 + 2 } \right)^2 + \left( {5 + 3 } \right)^2 }[/tex]
d = 8.544
Roud to nearest tenth ⇒ 8.54 units.
Hence "The distance between A(1,5) and B(-2,-3) is 8.54 rounded to the nearest tenth".
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3^4×2^3×3^7×2^2÷2^2×3^2×2^5×3^6
Answer:
the answer is
[tex] \frac{27}{4} [/tex]
A number is divided by 2, and then the quotient is increased by 8. The result is 33.
OA) / +8=33; 0.08
OB) +8=33; 50
OC)/2+8=33; 82
OD)-8=33; 82
Need help with this question?
The dividend is 50 , the quotient is 25 .
Let the no . ( the divisor ) be x .
Forming linear equation in one variable using given info .
Given : divisor = 2 , result = 33 , quotient increased by 8 .
Division Formula : Dividend = Divisor * Quotient .
Hence , the equation is ,
( x / 2 ) + 8 = 33
( x / 2 ) = 25
x = 50
Hence the dividend is 50 .
The quotient is 25 .
Therefore , option B ) is correct + 8 = 33 ; 82 .
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Collaborate
CSP Use Math Tools Work with a partner. If the measure of 21 in
the figure at the right is 40°, determine the measure of each given
angle without using a protractor. Then check your answers by
measuring with a protractor.
1. 22
3. 24
5. 26
7. 28
2. 23
4. 25
BeacO0CCO
6. 27
>
The measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.
What is an angle?The angle is the separation of the crossing surfaces or lines. Additionally, the angle is specified in degrees. One whole spin has an arc of 360 degrees.
If the total of two angles is 180 degrees, they are said to be supplementary angles.
In the third line, if two lines are parallel. Equal angles are formed by matching angles.
When two lines intersect, then their opposite angles are equal.
The measure of angle ∠1 is 40°.
Angle ∠1 and angle ∠2 are supplementary angles. Then the measure of angle ∠2 will be
∠1 + ∠2 = 180°
40° + ∠2 = 180°
∠2 = 140°
The vertical angles are given below.
∠1 = ∠3 = 40°
∠2 = ∠4 = 140°
The corresponding angles are given below.
∠1 = ∠5 = 40°
∠2 = ∠6 = 140°
∠3 = ∠7 = 40°
∠4 = ∠8 = 140°
Then the measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.
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Solve each equation or inequality.
4 x+6 ≥ -6
After solving for equation or inequality 4 x+6 ≥ -6, the value of x ≥ -3
⇒ 4 x+6 ≥ -6
⇒ 4x ≥ -6-6
⇒ 4x ≥ -12
⇒ x ≥ -12/4
⇒ x ≥ -3
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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W/6 + 7.2 = -2.4
Solve for W
Answer:
W = -57.6 PS: I'm in 8th grade.
Step-by-step explanation:
W/6 + 7.2 = -2.4 Step 1: Use Inverse operations (subtract 7.2 on both sides)
W/6 = -2.4 - 7.2 Step 2: Combine Like terms (-2.4 - 7.2)
W/6 = -9.6 Step 3: Use Inverse Operations (multiply by 6 on both sides)
W = -9.6 x 6 Step 4: Simplify
W = -57.6
Susie and friends rent 3 life jackets and a boat. The life jacket rents for $5.00 each. The boat rents for $25.00 per hour. The total cost is $115.
What is an equation that can be written to represent this situation? Explain your steps.
