RECALL
Set 4: Given the center and a point on the circle.
Distance Formula
13. center. (9, 10),
point on circle: (7,4)
15. center: (2,-6),
point on circle: (1,10)
Midpoint Formula
14. center: (1.-5),
point on circle: (-7.-13)
16. center: (-2, 0),
point on circle: (-9,-4)
Answers
Distance is the measure from one point to another point. Given, any two points distance is [tex]\sqrt{(x1-x2)^{2} }+\sqrt{(y1-y2)^{2} }[/tex].
Define Midpoint.Midpoint is the mid-value of two points.
Midpoint = [ x₁+x₂/2 , y₁+y₂/2]
So, for the given centre (9, 10) and point on circle(7,4)
Centre = [tex]\sqrt{}[/tex](9-7)²+(10-4)²
= [tex]\sqrt{}[/tex]4+36
= 6.32
For the given centre (2,-6) and point on circle (1,10)
Centre = [tex]\sqrt{}[/tex](2-1)²+(-6-10)²
=[tex]\sqrt{}[/tex]1+256
=16.03
For given centre (1,-5) and point on circle(-7,-13)
Midpoint = [ 1-7/2 , -5-13/2]
= [-3, -9]
For given centre(-2,0) and point on circle(-9,-4)
Midpoint = [-2-9/2 , 0-4/2]
= [-5.5,-2]
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Given, center (9,10) and point on circle is (7,4) distance is 6.32. And center (2,-6) and point on circle (1,10) distance is 16.03.
Given center (1, -5) and point of circle(-7,-13) midpoint is (-3,-9). And center (-2,0) and point on circle (-9,-4) midpoint is (-5.5,-2).
What is Distance and midpoint?Distance is the measure from one point to another point. Given, any two points distance is -
[tex]\sqrt{x_1^2-x_2^2} +\sqrt{y_1^2-y_2^2}[/tex]
Midpoint is the mid-value of two points. Midpoint = [(x₁+x₂)/2, (y₁+y₂)/2]
So, for the given center (9, 10) and point on circle(7,4)
Center = (9-7)²+(10-4)²
= 4+36
= 6.32
For the given center (2,-6) and point on circle (1,10)
Center = (2-1)²+(-6-10)²
= 1+256
= 16.03
For given center (1,-5) and point on circle(-7,-13)
Midpoint = [ 1-7/2 , -5-13/2]
= [-3, -9]
For given center (-2,0) and point on circle(-9,-4)
Midpoint = [-2-9/2,0-4/2]
= [-5.5,-2]
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Related Questions
(-4)³·7⁰
_____ this a fraction!
(-1³)
Answers
Anybody good at statistics that’s can help outside of here?
Answers
I'm here trying to help my 12 yr old
25% of 24 is what number
Answers
Answer: 6
Step-by-step explanation: you can ask siri
Multiply 24 x 0.25
the perimeters of the square and the rectangle below are the same. Write and solve an equation to find the value of x area= 121inches squared the rectangle is 3x and x-2
the area of the square is 121 in. Squared.
Answers
The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The borders of the square and the square shape underneath are something similar.
Perimeter of the square = Perimeter of the rectangle
4a = 2(L + W)
2a = L + W
If the area of the square is 121 square inches. Then the side length of the square is given as,
a² = 121
a = 11 inches
And the dimension of the rectangle is 3x and x - 2. Then the equation is given as,
3x + x - 2 = 11 (2)
4x - 2 = 22
4x = 24
x = 6
The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.
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Solve the following inequality and graph the solution:
(x-4)(x-5)<0
Choose test values and indicate whether the inequality is true or false in each region.
Enter the test values from smallest to largest.
Answers
The smallest to largest test values of the inequality (x-4)(x-5)<0 are
(-infinity,4) , (4,5) & (5,+infinity)
What is a inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.
"A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">," "," "," or "."
(x-4)(x-5)<0
x-4<0 or x-5<0
x<4 or x<5
1)
for False the test values of the inequality (x-4)(x-5)<0 from smallest to largest Lies in between (-infinity,4)
2)
for True the test values of the inequality (x-4)(x-5)<0 from smallest to largest Lies in between (4,5)
3)
for True the test values of the inequality (x-4)(x-5)<0 from smallest to largest Lies in between (5,+infinity)
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If g'(x) = (2-x)x² So how many extreme points does the function g(x) has?
Answers
There are 3 extreme points does the function g(x) = (2 - x) x².
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The function is,
⇒ g ' (x) = (2 - x) x²
Now,
Since, The function is,
⇒ g ' (x) = (2 - x) x²
We know that;
The extreme points are find as;
⇒ g ' (x) = 0
So, We get;
⇒ g ' (x) = 0
⇒ (x - 2) x² = 0
This gives two values as;
⇒ (x - 2) = 0
⇒ x = 2
And, x² = 0
⇒ x = 0, 0
Thus, The extremes values are;
⇒ x = 2 , 0, 0
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Given m∠1≅m∠2
Proof m∠3≅m∠4
Complete the flow chart to proof m∠3≅m∠4
Answers
The flow chart to prove m∠3≅m∠4 is given below.
What is the vertical angle theorem?
The Vertical Angle Theorem states that when two straight lines cross, they create two linear pairs. Due to the fact that their angles add up to 180 degrees, the adjacent angles created when two lines intersect are known as supplementary angles.
Given, m∠1≅m∠2
Then, m∠1≅m∠3 ( vertical angles theorem)
m∠2≅m∠3 (Given)
Then, m∠2≅m∠4 (vertical angle theorem)
Hence, m∠3≅m∠4 (transitive property of congruence) proved
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Cameron invests money in a bank account
which gathers compound interest each year.
After 4 years there is $736.80 in the account.
After 7 years there is $788.82 in the account.
Work out the annual interest rate of the bank
account.
Give your answer as a percentage to 1 d.p.
Answers
The annual interest rate of the bank account is 2.3%
Let's check the equation for each year.
Compound Interest earned amount
A = P( 1 + r/n)ⁿˣ
A = accumulated amount
P = original amount deposited
r = interest rate
n = times it compounds per year
x = years
when Amount = $736.80, x = 4 years and r% → r/100
736.80 = P(1 +[(r/100)/1] ¹×⁴
736.80 = P(1 + r/100)⁴
when Amount =$788.82 , x = 7 years and r% → r/100
788.82 = P(1 +[(r/100)/1] ¹×⁷
788.82 = P(1 + r/100)⁷
using the 1st equation:
736.80 = P(1 + r/100)⁴
P = 736.80 /[(1 + r/100)⁴]
Substitute on the Using 2nd equation
788.82 = P(1 + r/100)⁷
788.82 = 736.80 /[(1 + r/100)⁴] * (1 + r/100)⁷
788.82 = 736.80 * [(1 + r/100)⁷/(1 + r/100)⁴]
788.82 = 736.80 * (1 + r/100)³
788.82/736.80 = (1 + r/100)³
∛788.82/736.80 = ∛ (1 + r/100)³
∛788.82/736.80 = (100 + r)/100
100 ∛788.82/736.80 = 100 + r
100 ∛788.82/736.80 - 100 = r
r ≈ 2.3%
Hence, the annual interest rate of the bank account is 2.3%
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Name the three types of triangles that deal with the measure of the sides
Answers
Find the amount that results from the given investment.
$600 invested at 6% compounded quarterly after a period of 4 years
After 4 years, the investment results in $.
(Round to the nearest cent as needed.)
Answers
We can tell that the investment results after 4 years will be $761 with the help of compound interest.
What is compounding?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it so that interest is generated the next period on the principal amount plus any accumulated interest.
In finance and economics, compound interest is common.
So, we have an initial investment of %600.
And the interest is 6% which will be compounded quarterly for 4 years.
Then the amount we will receive after 4 years is:
(Refer to the table attached below)
So, the amount we will get after 4 years is $761.39.
Rounding off: $761
Therefore, we can tell that the investment results after 4 years will be $761 with the help of compound interest.
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What is calculas of variations?
Answers
Answer:
Hey there!
Step-by-step explanation:
This is ur answer...
The calculus of variations is a field of mathematics about solving optimization problems. This is done by minimizing and maximizing functionals. The methods of calculus of variations to solve optimization problems are very useful in mathematics, physics and engineering.
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23. For the data in the table, does y vary directly with x? If it does, write an equation for the direct (1 point) variation.
yes; y=2 x
yes; y=5 x
yes; y=7 x
no; y does not vary directly with x.
Answers
The ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.
What is the constant of variation?
The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.
We have,
x y
2 10
4 24
6 36
To determine whether y varies directly with x, you need to see if the ratio of y to x is constant for all the data points.
If y varies directly with x, then the ratio y/x will be constant for all the data points. In this case, you can write an equation for the direct variation in the form y = kx, where k is the constant of variation, which is equal to the ratio y/x.
If the ratio y/x is not constant for all the data points, then y does not vary directly with x.
so, let's see the k constant of variation,
k = y/x
k = 2/10 =1/5
k = 4/24 = 1/6
k = 6/36 = 1/6
so, k = 1/5, k=1/6, k=1/6.
Hence, the ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.
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Dontrell bought 51/2 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.
Answers
The equation that represents the the total amount he paid, y, for x pounds of potatoes is y = 0.64x.
How to use equation to represent the total amount paid?Dontrelle bought [tex]5\frac{1}{2}[/tex] pounds of potatoes for $3.52.
The equation that can be used to represent the the total amount he paid, y, for x pounds of potatoes is as follows:
rate = amount paid / weight in pounds
amount paid = $3.52
weight of potatoes = 11 / 2 pounds
rate = 3.52 ÷11 / 2
rate = 3.52 × 2 / 11
rate = 7.04 / 11
rate = 0.64 dollars per pound.
Therefore, the equation is y = 0.64x
where
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A cable company offers its customers two plans.
- Plan A costs $135 per month plus $15 for each premium channel.
- Plan B uses the equation C=5 p+180 to determine the cost, where C represents the total cost and p represents the number of premium channels.
If a customer wants 5 premium channels, which statement comparing the cost of Plan A and Plan B is true?
A. Plan A will cost $5 less than Plan B.
B. Plan A will cost $10 less than Plan B.
C. Plan A will cost $5 more than Plan B.
D. Plan A will cost $10 more than Plan B.
Answers
After solving the equation we can say that Plan A will cost $10 more than Plan B. So, D is the Correct answer
What is an Equation?
A statement that affirms the equality of two expressions connected by the equals sign "=" is known as an equation.
For illustration, 2x - 5 = 13.
The two most well-known groups of equations in algebra are the linear
equations and the polynomial equations.
P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations.
Here, the parameters a and b. To solve these equations, we can use geometric or computational techniques from linear algebra or mathematical analysis. There are several sorts of equations
as well, including:
linear algebra quadratic formulas cube-based equations linear equations Equations that differ Statistical equations
Plan A:- $135 + $15(no. of premium channel)
Plan A for 5 premium channels will be
=$135 + $15(5)
= $135 + $75
=$210
Plan B:-
equation
C=$(5p+180)
p = no. of premium channel
Plan B for 5 premium channels will be equation
C = $25 + $180
= $205
Thus,
Plan A will cost $5 more than Plan B
As Plan A cost $210 and Plan B cost $205
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help please no need to do alot of steps
Answers
[tex]x = \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex] , [tex]x = -\sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]
Step-by-step explanation:
[tex]z= -9+3x^{2} +3y^{2} : x= \sqrt{\frac{z-3y^{2}+9 }{3} } ,x = - \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]
[tex]z= -9+3x^{2} +3y^{2}[/tex] : [tex]-9+3x^{2} +3y^{2} =z[/tex]
[tex]-9+3x^{2} = z- 3y^{2}[/tex]
[tex]3x^{2} = z - 3y^{2} +9[/tex]
[tex]\frac{3x^{2} }{3} = \frac{z}{3} - \frac{3y^{2} }{3} + \frac{9}{3}[/tex]
[tex]x^{2} = \frac{z-3y^{2}+9 }{3}[/tex]
for [tex]x^{2} =[/tex][tex]f(a)[/tex] the solutions are [tex]x= \sqrt{f(a)} , -\sqrt{f(a)}[/tex]
[tex]x = \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex] , [tex]x = -\sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]
[tex]x = i \sqrt{\frac{z+2y^{2}-5 }{2} } , x = -i \sqrt{\frac{z+2y^{2}-5 }{2} }[/tex]
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GIVING BRAINLIEST!!!
What fraction is shown on the number line?
A. 2 over 3
B. 1 over 3
C. 2 over 4
D. 3 over 4
Answers
Answer:
a
Step-by-step explanation:
Answer:a
Step-by-step explanation:
7.1.1 use the results of section 3.7 to show that each member of isom (r2) is either a translation or a rotation. 7.1.2 why does an isometry map any circle to a circle? we took care to write the inverse of the isometry r1r2r3 as r3r2r1 because only this ordering of terms will always give the correct result. 7.1.3 give an example of two reflections r1 and r2 such that r1r2
Answers
Every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.
Given that,
Show that each component of isom (r²) is either a translation or a rotation using the findings from section 3.7.
An isometry of R² is a mapping T:R²⇒R² which preserves distance.
The formula for the distance between x and y is
d(x,y)=|y-x|=√(y₂-x₂)²+(y₁-x₁)²
The preservice means,
d(x,y)=d(T(x),T(y))
A translation is an isometry.
Since,
d(Tv(x),Tv(y))=|(xv)-(y-v)|=d(x,y)
The rotation matrix, for rotating by an angle Θ, is defined as,
cosΘ -sinΘ
sinΘ cosΘ
Therefore, every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.
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Solve one eighth times quantity x plus 32 end quantity equals negative 7.
HURRY 100 PTS
x = 56
x = 7
x = −88
x = −24
Answers
The solution of the expression will be;
⇒ x = - 88
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
'' one eighth times quantity x plus 32 end quantity equals negative 7.''
Now,
Since, The algebraic expression is,
'' one eighth times quantity x plus 32 end quantity equals negative 7.''
Hence, We can formulate;
⇒ 1/8 (x + 32) = - 7
⇒ x + 32 = - 56
⇒ x = - 56 - 32
⇒ x = - 88
Thus, The solution of the expression will be;
⇒ x = - 88
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which ordered pair is the solution y=(1/3)x-4
Answers
To find the ordered pair that is the solution to the equation y = (1/3)x - 4, we need to solve the equation for x.
To do this, we can first add 4 to both sides of the equation to get y + 4 = (1/3)x. Then, we can multiply both sides of the equation by 3 to get 3y + 12 = x.
Therefore, the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 3y).
Note that the value of y is unknown in this solution. In order to find the exact solution, we would need to know the value of y. For example, if y = 2, then the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 6).
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 7 liters of synthetic oil. In order to make 825 liters of Petrolyn oil, how many liters of natural oil are needed?
Answers
The natural oil that will be needed to make make 825 liters of Petrolyn oil is 300 liters.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this situation, Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 7 liters of synthetic oil. In order to make 825 liters of Petrolyn oil, the natural oil will be:
= 4 / (4+7) × 825
= 4 / 11 × 825
= 300
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Write a
system of equations with the solution (4, -3).
Answers
Answer:
A (0, -3) translated to the right 4 units.
Step-by-step explanation:
If you go right 4, you get (4, -3)
Judy wants to buy a sandwich platter. Every 6 inches of sandwich costs $2.50. What is the total
cost in dollars if Judy buys 18 inches?
Answers
Answer:
[tex]\huge\boxed{\sf \$ 7.50}[/tex]
Step-by-step explanation:
Given that,
6 inches of sandwich = $2.50
Multiply 3 to both sides
6 × 3 inches of sandwich = $2.50 × 3
18 inches of sandwich = $7.50[tex]\rule[225]{225}{2}[/tex]
To allow last minute christmas shopping silverburn shopping centre is opening from 8am till midnight on Monday to Saturdays and 8am till 10pm on sundays. How many hours is it open in one week
Answers
if c is (5x-7) degrees and b is (8x-55) degrees what is the value of x
Answers
The value of x is 18 if ∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.
What are vertically opposite angles?
It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
It is given that:
∠C and ∠D are vertical angles.
From the definition of the vertically opposite angles:
5x-7 = 8x-55
After solving we get:
-7 = 3x -55
3x = 48
x = 16
Thus, the value of x is 18 if ∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.
The complete question is:
∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55. What is m∠D ?
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A force of 400 newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion.
Answers
The equation of motion for the mass attached to the spring
x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2
What is the equation of motion?Generally, The equation of motion for a mass on a spring is given by Hooke's law, which states that the force exerted by a spring is proportional to its displacement from equilibrium. The proportionality constant is known as the spring constant, which is denoted by the letter k.
In this case, the force exerted by the spring is 400 newtons, and the displacement from equilibrium is 2 meters. Therefore, the spring constant is given by:
k = F/x = 400 N/2 m = 200 N/m
The equation of motion for a mass on a spring is given by:
F = ma = -kx
where F is the force exerted by the spring, m is the mass of the object, a is the acceleration of the object, and x is the displacement of the object from equilibrium.
Substituting the values for the spring constant and the mass, we get:
-kx = -(200 N/m)(50 kg)(x'')
Solving for the acceleration, we get:
x'' = -k/m = -200 N/m / 50 kg = -4 m/s^2
This is the equation of motion for the mass attached to the spring. The negative sign indicates that the acceleration is in the opposite direction of the displacement, as is expected for a mass on a spring.
Finally, to find the equation of motion, we need to take into account the initial velocity of the mass. The equation of motion for an object with initial velocity is given by:
x = x_0 + v_0t + (1/2)at^2
where x is the displacement of the object, x_0 is the initial displacement (in this case, the equilibrium position of the spring), v_0 is the initial velocity, t is time, and a is the acceleration.
Substituting the values for the acceleration and the initial velocity, we get:
x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2
This is the equation of motion for the mass attached to the spring. The initial displacement, x_0, is the equilibrium position of the spring, which is assumed to be at x=0 in this case.
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Answers
Based on the information in the fragment, it can be inferred that Josiah's mistake is that he did not multiply the numerator and denominator by the correct number to equal 1,500 (option B). So, the correct statements are A, C, and D.
How to find the ratio?To find the proportion in this problem we have to do the following procedure:
The first step is multiply both sides by 1500.The second step is to evaluate the expression on the right-hand side.The third step is multiply 10 by 1500 on the left-hand side.The fourth step is divide 15000 by 20 on the left-hand side.Once we have carried out the previous steps we must continue the procedure rewriting the equation with the data obtained previously. With this information we can conclude that Josian had the necessary information to discover how many songs of each genre were played during an hour on his MP3, however he performed the wrong procedure so his result was wrong.
According to the above, we can infer that the products are not well carried out. So, Josiah's mistake is no multiplying the numerator and denominator by the correct number to equal 1,500 (option B).
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Please help!
A basketball has the radius of 13 inches
What is the volume?
Answers
Answer:
9203 in.³
Step-by-step explanation:
V = (4/3)πr³
V = (4/3) × 3.14159 × (13 in.)³
V = 9203 in.³
an exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is currently 100 feet below the sea level. How deep was the diver 15 minutes ago?
Answers
and x=minutes
so 25 minutes multiplied by 15 is 375 and he’s 100 below right now so 375+100=475 therefore he was 475ft. below sea level
Organize the angles from largest to smallest.
Answers
Triangle congruence
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Answers
If we reflect triangle XOF back into DOG, we see that sides DO and OF are corresponding side, as so are sides GO and OF. Therefore, these sides are congruent.
DO ≅ OF
Substitute the expressions in for the side lengths:
(10-2x)=(7x-2)
Solve for x:
10=7x+2x-2
10+2=9x
12=9x
12/9=x
x=1.333
GO ≅ OX
Substitute the sides in:
(8y+3)=(16-6y)
Solve for y:
8y+6y+3=16
14y=16-3
14y=13
y=14/13
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