The radius is 169 inches.
As per the known fact, the radius and area of circle are related by the formula -
Area = πr²
So, rewriting the expression in equation -
r=√(A/π)²
As mentioned, r is the radius and A is the area of the circle and π is constant
Keep the value of A in the above mentioned rewritten equation to find the value of radius of circle.
r = √(169π/π)²
On solving the above equation we get the new equation, which is as follows -
r = 169π/π
Cancelling π as it is common in both numerator and denominator
r = 169 inches
Hence, the radius of circle is 169 inches.
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Lloyd bought two pumpkins. On a coordinate grid, he plotted each pumpkin’s weight (x), in ounces, and price (y), in dollars. He then drew a straight line that passed through both points and the origin. The line he drew also passed through the point (1, n) for some number n. What does the number n represent?
Since the line Lloyd drew also passed through the point (1, n) for some number n, the number n represents: (A) the price, in dollars, per ounce of pumpkin.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the points on a cartesian coordinate are generally written as an ordered pair (x, y) which represents the horizontal line and vertical line respectively.
Since the line Lloyd drew also passed through the point (1, n) for some number n, we can reasonably infer and logically deduce that the number n represents the price, in dollars, per ounce of pumpkin.
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Complete Question:
Lloyd bought two pumpkins. On a coordinate grid, he plotted each pumpkin’s weight (x), in ounces, and price (y), in dollars. He then drew a straight line that passed through both points and the origin. The line he drew also passed through the point (1, n) for some number n. What does the number n represent?
(A) the price, in dollars, per ounce of pumpkin
(B) the price, in dollars, of one of the pumpkins
(C) the weight, in ounces, of one of the pumpkins
(D) the weight, in ounces, of a pumpkin with a price of $1.00
2. The vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).
a. Find the equation of the perpendicular bisector of the side QR.
b. Find the slope of the median of the triangle that passes through point R.
c. Find the slope of the altitude of the triangle that passes through point Q.
The answers will be :
a. The equation of perpendicular bisector of QR is y = [tex]\frac{-5}{3}[/tex] x + 3.
b. The slope of median of triangle passing through point R is 1/4.
c. The slope of the altitude of the triangle that passes through point R doesn't exists.
What is slope of a line segment ?
Slope is the ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.
It is given that the vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).
a.
The midpoint (M) of QR will be equal to
( [tex]\frac{-2 + 8}{2} , \frac{-5 + 1}{2}[/tex] )
or
M = (-3 , 2)
Now , slope of line QR will be ;
[tex]m_{QR}[/tex] = [tex]\frac{1+5}{8+2}[/tex]
[tex]m_{QR}[/tex] = 6 / 10
We know that :
m × [tex]m_{QR}[/tex] = -1
m = -10 / 6
or
m = -5 / 3
Equation of line will be given as :
y + 2 = [tex]\frac{-5}{3}[/tex] ( x - 3 )
y = [tex]\frac{-5}{3}[/tex] x + 3
b.
The midpoint of PQ will be :
= ([tex]\frac{-6 - 2}{2} , \frac{1 - 5}{2}[/tex])
= ( -4 , -2)
The slope of median of triangle that passes through point R will be ;
m = [tex]\frac{-2 - 1}{-4-8}[/tex]
m = -3 / -12
m = 1/4
or
m = 0.25
c.
Slope of altitude of triangle that passes through point Q will be :
m = [tex]\frac{1 - 1}{-6-8}[/tex]
m = 0 / -14
m = 0
The slope in this case doesn't exist.
Therefore the answers will be :
a. The equation of perpendicular bisector of QR is y = [tex]\frac{-5}{3}[/tex] x + 3.
b. The slope of median of triangle passing through point R is 1/4.
c. The slope of the altitude of the triangle that passes through point R doesn't exists.
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3m² + n; m = 5, n = 3
HELP ME plsss show with work ! thank u !!
Answer: .8 or 4/5
Step-by-step explanation:
You can do this a couple ways.
1) what you started is right, you can change your fraction into a decimal and divide.
2/5 = .4
.32/.4 = .8
2) you can change .32 into 32/100 and divide by 2/5
32/100 divided by 2/5
When you divide fractions, you flip the divisor and multiply
32/100 x 5/2
Multiply across
160/200
Simplify
4/5
The school paper says that no less than a third of the juniors went to prom. If 37 juniors went, then what is the minimum amount of juniors at the school?
Based on the fact that no less than a third of the juniors went to prom and there were 37 juniors, the minimum amount of juniors at the school was 111 juniors
How to find the juniors who went to prom?The school paper reported that out of the total juniors in school, no less than a third juniors went to prom.
We also know that 37 juniors went to prom. Assuming that 37 juniors represents a third of the juniors, the minimum amount of juniors at the school can be found as:
= Number of juniors who went to prom / Proportion of juniors who went to prom
Solving for the minimum amount of juniors at the school gives:
= 37 / 1/3
= 37 x 3/1
= 111 juniors
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Subject - Geometry
Please Help
Answer:
for the first question,i cannot help since the picture is not clear,but for the second one,i can.so here is the answer for the second question2(-2)+6=22(0)+6=62(2)+6=102(4)+6=14Step-by-step explanation:
u just need to replace the (x) in the equalition.on the calculator,u just write the equalation normally but when u want to replace the ( x) u have to put bracket.replace the x with number next to it or the number at x box.u can check again my answerThe length of a rectangle is 6 meters more than three times the width. The perimeter of the rectangle is 44 meters. What are the dimensions of the rectangle?
Answer:
Hey! the breadth is 12 m and the length is 12+6=18 m
Mark me as brain?
Step-by-step explanation:
let the breadth be X metre
so the length will be 6+ x metre
perimeter is equal to 60 m
2(6+x+x)=60
2 (6+2x)=60
12+4x=60
4x=60-12=48
x=48/4=12
so
- What is the density of an object whose mass is 180 grams and whose volume is 45 cm
B. 0.25 g/cm³
A. 4 cm³/g
C. 4 g/cm³
D. 0.25 cm³/g
The density of an object with a mass of 180 grams and a volume of 45 cm is 0.4 kg/m.
What is density?
How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.So the formula will be d = m / v
The mass of the object is 180 g
The volume of the object is 45 cm
Putting the value in the formula
d = 180 g / 45 cm = 0.4 kg/m
Thus, the density of an object will be 0.4 kg/m.
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10. The distance between the points (5, 7) and (8, -5) is
a) √153
b) √ 154
c) √13
d) √53
Answer:
i THINK im not sure but i think its C please let me know if im wrong
Step-by-step explanation:
Solve each equation. Check for extraneous solutions. √5 x+1 -2√x=1
The solution of the equation √5 x + 1 - 2√x = 1 is [tex]\frac{4}{5}[/tex].
An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
Consider the equation,
√5 x + 1 - 2√x = 1
Subtracting 1 from each side of the equation.
√5 x + 1 - 2√x - 1 = 1 - 1
√5 x - 2√x = 0
√5 x = 2√x
Dividing each side of the equation by √x.
( √5 x/√x ) = ( 2√x / √x )
√(5x) = 2
Squaring each side of the equation.
[ √(5x) ]² = (2)²
5x = 4
Dividing by 5 from each side of the equation.
( 5x/5 ) = ( 4/5)
x = 4/5
Now checking the extraneous solution:
[tex]\sqrt{5}x + 1 -2\sqrt{x} =1\\\sqrt{5}(\frac{4}{5} ) + 1 - 2(\sqrt{\frac{4}{5} } ) = 1\\ \frac{4}{\sqrt{5} } + 1 - \frac{4}{\sqrt{5} } = 1\\ 1 = 1[/tex]
The solution for the equation is 4/5.
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Suppose two friends are standing next to each other. One friend runs 35.7 yards in one direction. The other friend runs 18.1 yards in the opposite direction, stops, and then continues in
the same direction for 10.5 more yards. How far apart are the friends?
8 is subtracted from the cube of a number.
Answer:Solution
Result will not divisible by 3
5
3
×2−8=250−8=242
If we divide 242 by 3 it will leave reminder 2.
Step-by-step explanation:
The equation is given by A = n³ - 8 , where n is a number
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number be represented as n
A = 8 is subtracted from the cube of a number
Substituting the values in the equation , we get
A = n³ - 8 be equation (1)
Now , when 8 is subtracted from twice the cube of 5 , the result is not divisible by 3
So , A = 2 x 5³ - 8
A = 242 which is not divisible by 3
Hence, the equation is A = n³ - 8
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"Evalúa 2x²+5 cuando x = 3"
Answer:
23
Step-by-step explanation:
x=3 PEMDAS says that exponents go first so 3x3=9 then 2x9=18+5=23
The sum of 5 and a number is then multiplied by two. The answer is -2 What is the number
What is the answer to this question?
Answer:
222
Step-by-step explanation:
What is the solution of each exponential equation? Check your answer.
a. 7⁻⁴x=800
Solution of exponential equation is , x = [tex]800. 7^4[/tex]
What is exponential equation ?In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]a^x[/tex] .
where, a = the base of function
x = main expression
Mathematically, if [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as [tex]a^x = N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.
Some important formulas of exponential :
[tex]a^x . a^y = a^{x+y}[/tex][tex]\frac{a^x}{a^y} = a^{x-y}[/tex][tex]a^x.b^x=(ab)^x[/tex][tex](a^x)^y = a^{xy}[/tex][tex]a^{-x} = \frac{1}{a^x}[/tex]According to given statement,
[tex]7^{-4} x = 800[/tex]
=> [tex]\frac{1}{7^4} x = 800[/tex]
=> [tex]x = 800 . 7^4[/tex]
Thus solution for this equation is x = [tex]800. 7^4[/tex]
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The complete question is :
What is the solution of each exponential equation? Check your answer.
a. 7⁻⁴x=800
b. 5.2³x=400
Simplify
6-√√25
4
DONE
11
The simplified expression of 6 -√25 + √4 is 3
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the expression?The expression is given as
6 -√25 + √4
Evaluate the exponents
So, we have
6 -√25 + √4 = 6 - 5 + 2
Evaluate the difference
So, we have
6 -√25 + √4 = 1 + 2
Evaluate the sum
So, we have
6 -√25 + √4 = 3
Hence, the simplified expression of 6 -√25 + √4 is 3
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Answer:
Step-by-step explanation:
6-√√25= 0.25
-2-√15/2= A, -2.94
x=5+√-49/6= C, 5/6+7/6i
Look at the diagram
Angle Diagram
3
A
B
23°
67°
(7x - 5)º
O
2
7
1 point
Which equation can be used to solve for x?
30x-5-67
30x+5-67
7x+18-67
7x+28-67
1 point
The equation that can be used to determine the value of x is 7x + 18 = 65
What are angles?Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the value of x?The figure that completes the question is added as an attachment
The given parameter is the angles in the figure
From the figure, we have the following angles:
Angle 1 = 23
Angle 2 = 7x - 5
Angle 3 = 67
The relationship between the above angles is
Angle 1 + Angle 2 = Angle 3
This is so because the angles 1 and 2 are adjacent angles and they add up to angle 3
Substitute the known values in the above equation
So, we have
23 + 7x - 5 = 65
Collect the like terms in the above equation
So, we have
23 - 5 + 7x = 65
Evaluate the like terms in the above equation
So, we have
18 + 7x = 65
Rewrite the above equation as
7x + 18 = 65
Hence, the equation that can be used to determine the value of x is 7x + 18 = 65
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i am do confused i am so sure I got it right but it marks it as wrong.
Answer:
Step-by-step explanation:
Try the code AEAA. Let me know if its right or not.
Answer:
CHGD
Step-by-step explanation:
You should actually solve each of these puzzles to get the right code
1. To evaluate f(-2)
We have f(x) = x³ - 2x
Substitute -2 for x
==> (-2)³ - (2 x-2)
-2³ = -8
2 x -2 = -4
==> f(-2) = -8 - (-4)
==> f(-2) = -8 + 4 (two negatives make a positive
==> f(-2) = -4 Letter C
2. Evaluate g(-10)
[tex]g(x) = \dfrac{3x}{2}[/tex]
[tex]g(-10) = \dfrac{3 \times -10}{2} \\= \dfrac{-30}{2} \\\\= \boldsymbol{-15}[/tex] Letter H
3. Evaluate h(-1)
h(x) = 2x² + x
h(1) = 2 x (-1)² - 1
= 2 x 1 - 1
= 1 Letter G
4. Evaluate f(3)
f(x) = x³ -2x
f(3) = 3³ - 2 x 3
= 27 - 6
= 21 Letter D
So the correct code is CHGD
You got everything right except the third :)
1) g(a)=a³+5a²
f(a)=2a +4
Find g(3) + f(3)
Answer:
82
Step-by-step explanation:
if g(3)= substitute a as 3 = (3)^3 +5(3)^2= 27+45= 72
if f(3)= substitute a as 3= 2(3) +4=10
join them up since it said there to add g(3) +f(3)
72 +10= 82
Assume you have applied for two jobs a and b. The probability that you get an offer for job a is 0. 25. The probability of being offered job b is 0. 20. The probability of getting at least one of the jobs is 0. 40. What is the probability that you will be offered both jobs? enter your answer as a decimal rounded to two places.
If you have applied for two jobs a and b and the probability that you get an offer for the job a is 0.25 and the probability of being offered job b is 0.20, then the probability that you will be offered both jobs is 0.05.
Probability is that branch of mathematics that deals with the numerical description of the possibility of an event to occur. The probability of any event is a number between 0 and 1 where 0 represents the impossibility of the event to occur while 1 represents certainty of that event to occur.
As the probability of the job a and job b are independent of each other, the probability that both jobs will be offered can be determined by using the formula;
P(A∩B) = P(A) × P(B)
Here, P(A∩B) represents the probability of both the events happening together
As P(A) = 0.25
P(B) = 0.20
P(A∩B) = 0.25 × 0.20
P(A∩B) = 0.05
Hence, the probability that both jobs will be offered is calculated to be 0.05.
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PLEASE HURRY!! APPROXIMATE THE VALUE AND CHOOSE CORRECT STATEMENT
The correct statements among given statements are statement C and E.
What is a rational number ?
If p & q are any two numbers where q is not equal to 0, then the fraction in form p/q is called as rational number.
A number is given which is √22.
√22 = 4.69041576
Let's check which of the statements are correct.
A.
√22 is not rational number as the number has non - terminating decimal value which is 4.69041576 and it doesn't lies between 10 and 12. So , this option is not correct.
B.
This option is also not correct as the value of √22 nearly equals 4.69 is and not greater than 4.691.
C.
The value of √22 is 4.69041576.
If we round off to the nearest hundredth , 9 is at the hundredth place , so the value will be 4.69. This is a correct option.
D.
√22 is not a rational number as the number has non - terminating decimal value which is 4.69041576 but it lies between 4 and 5. So , this option is not correct.
E.
The value of √22 is 4.69041576. We can observe that the decimal number doesn't repeat. So , this is a correct option.
F.
As we know √22 is not a rational number we can't represent it as fraction. This option is not correct.
Therefore , the correct statements among given statements are statement C and E.
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Fill in the Blank
The point-slope form of the equation for a line with slope m and passing through point (x₁, y₁) is ____
Answer:
(y - y1) = m(x - x1)
Step-by-step explanation:
(y - y1) = m(x - x1)
Make n the subject of this formula:
W= an + Z
Answer:
n = (W - Z)/a
Step-by-step explanation:
W = an + Z
Rearrange the equation so that the subject is alone, in the format Ax = B
W = an + Z
W - Z = an + Z - Z
W - Z = an
Isolate the subject by dividing or multiple so that the equation is in the format x = C
W - Z = an
(W - Z)/a = an/a
(W - Z)/a = n
Equation practice with angle addition
Given f(n)=7n-5
Evaluate f(-3)
GIVING BRAINLIEST
Answer:
f(-3) = -26
Step-by-step explanation:
f(n)=7n-5; f(-3)
f(-3) = 7(-3) - 5
f(-3) = -21 - 5
f(-3) = -26
I hope this helps!
Multiply if possible. Then simplify. ∛-7. ∛49
The value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.
We are given the expression:
∛ - 7. ∛ 49
We need to multiply and simplify it.
We will first multiply the expression:
= ∛ - 7 × 49
Solving it, we get that:
= ∛ - 343
Now this can also be written as:
= ∛ (- 7 )³
Now, simplifying the cube root to get the value of the expression:
= - 7
Therefore, we get that, the value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.
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Suppose x and y vary inversely, and x=8 when y=-7 .
a. What is the function that models the inverse variation?
The function that models the inverse variation is y = -56/x.
What exactly is the inverse variation?Inverse variation refers to a relationship between two variables in which the value of one increases while the value of the other decreases.When two quantities, say X and Y, are related in such a way that increasing X causes a decrease in Y and vice versa, this is known as indirect or inverse variation.So,
In an inverse function: x · y = C where C is the constant.Then,
-7 · 8 = -56 = CSince x · y = C then we obtain:
x · y = -56 ⇒ y = -56/xTherefore, the function that models the inverse variation is y = -56/x.
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A flower shop sells 21 different bouquets and multiple different styles of vase. Which are the possible numbers for the total number of combinations of bouquet and vase?
The first three rooms took the painter a total of 9 hours to paint. If the learning curve rate is 85%, how long will it take the painter to paint all 20 rooms in stately wayne manor?.
It will take the painter more than 40 hours to paint all 20 rooms in stately wayne manor .
Time taken for the first 3 rooms =9hrs
Learning curve rate = 85%
Time taken for the next 20 rooms =?
Time taken for 1 room = 9hrs / 3 rooms = 3 hrs
If it takes 3 hrs to paint 1 room
Therefore, it will take x hrs to paint 20 rooms would take;
Hence, 20 rooms multiplied 3 hrs = 60 hours
It may take 60 hours to complete painting the 20 rooms.
At a learning curve rate of 85%, 15% will be the progress rate
Therefore, it will take additional 15% of 60 hours to paint the 20 room.
60+9(15% of 60) =69 hours
The painter would take more than 40 hours to paint the 20 rooms given his efficiency and learning curve rate. The answer is derived by relating the data provided in the question to the desired answer.
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