Answer:
Option B. 25 ft
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=157\ ft[/tex]
assume
[tex]\pi =3.14[/tex]
substitute in the formula
[tex]157=2(3.14)r[/tex]
Solve for r
Divide by 2(3.14) both sides
[tex]r=157\(2(3.14))[/tex]
[tex]r=25\ ft[/tex]
The sum of three numbers is 50. one number is 10 more than the second number it’s also twice the third find the number
The three numbers will be 24, 14 and 12 respectively.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is the sum of three numbers is 50 and first number is 10 more than the second number and it is also twice the third.
Assume that the three numbers are [x] , [y] and [z].
Then, we can write -
x + y + z = 50 ..[1]
x = y + 10 ..[2]
x = 2z ..[3]
Equating Eq [2] and Eq [3], we get -
2z = y + 10
Rearranging the equation above -
y = 2z - 10
Now, for Eq [1], we can write -
2z + z + y = 50
3z + y = 50
3z + 2z - 10 = 50
5z = 60
z = 12
Then, the value of [y] will be -
y = 2 x 12 - 10
y = 24 - 10
y = 14
and
x = 2z = 2 x 12 = 24
Therefore, the three numbers will be 24, 14 and 12 respectively.
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Find an equation of the vertical line that passes through (x, y) = (−7, 1).
Take a look at the figure. What is the first step you should take to solve the formula?
A. Find the value of 6 squared. B. Cancel 6 into 6. C. Subtract 2 from 3. D. Multiply 3 by 6.
Helpppppppppppppppppppppppppppppp
replace the numbers inside () for x
f(4) = -4(4)-3 = -16 -3 = -19
G(-4) = 2(-4)^2 -3(-4) = 44
Lindsey has 45ft of metal fencing to form 3 sides of a rectangular garden. A tall wooden fence already in place will serve as the fourth side. What lengths of fencing will produce the largest area?
To maximize the area of a rectangular garden with one side already fenced, Lindsey should allocate the 45 ft of fencing available to form the remaining three sides in a way that makes the two lengths and the width as equal as possible. While an exact numerical answer depends on additional constraints, the guiding principle is that a more square-like configuration will yield the largest area.
Explanation:The question asks what lengths of fencing will produce the largest area for a rectangular garden, given that Lindsey has 45 ft of metal fencing and an existing tall wooden fence will serve as one side of the rectangle. To maximize the area enclosed by a given perimeter, which in this case is the length of the fencing available for three sides of the rectangle (since one side is already in place), it is beneficial to review a principle regarding geometric figures and their areas.
It is a well-established mathematical principle that of all rectangles with a given perimeter, the square has the largest area. However, since one side is already provided and Lindsey is forming only three sides of the rectangle, the problem slightly deviates from forming a perfect square. Nonetheless, the principle that more equidistant lengths result in larger areas can guide us to maximize the area Lindsey can enclose.
Lindsey has 45 ft of fencing to create three sides of a rectangle. For simplicity, let's denote the lengths of the two equal sides as L, and the length of the third side (parallel to the existing fence) as W. Since the total length of fencing is 45 ft, the equation we have is 2L + W = 45. To maximize the area (A = L*W), Lindsey should opt for dimensions where L and W are as close as possible to each other within the constraint of the given perimeter (or in this case, the total length of fencing available).
However, without additional constraints (like the length of the existing fence), a definitive numerical answer cannot be provided. The general advice for Lindsey is to distribute the length of the fencing as evenly as possible between the two lengths and the width she needs to create, thereby approximating a square's dimensions which tends to maximize the enclosed area.
what are the angle measures of the triangle? a)30, 60, and 90 b)45, 45, and 90 c)60,60,and 60 d)they cannot be determined.
the right answer is actually 30,60,90, I got the answer right on the test
The measures of the angles are 30°, 60°, and 90° for the given right triangle. The correct answer would be option (A).
What is right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
The right triangle is given in the figure, as shown.
According to the figure,
perpendicular = 7√3
hypotenuse = 14√3
As per the question, we have
Since sin θ = perpendicular/hypotenuse
Substitute the values in the above formula, and we get
sin θ = 7√3/14√3
sin θ = 1/2
θ = 30°
This means the measures of the angles are 30°, 60°, and 90°.
Hence, the correct answer would be an option (A).
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The question seems to be incomplete, the missing part has been attached below.
What is the average rate of change of the function on the interval from x = 1 to x = 2?
f(x)=10(5.5)x
x=1 f = 10(5.5)(1) = 55
x=2, f = 10(5.5)(2) = 110
110-55 = 55
2-1 =1
55/1 = 55
average rate of change = 55
a major stadium has 45,000 seats. fans bought 5/8 of the seats. how many seats are left?
fans bought 5/8 so there is 3/8 still left
45000 * 3/8 = 16,875 seats are left
I have another math question
Can you check if I did this right? (:
△FEB≅△CNB.
What is length of BN¯¯¯¯¯¯ ?
we know that
The CPCTC states that corresponding parts of congruent triangles are congruent
so
△FEB≅△CNB
that means
[tex]FE=CN\\FB=CB\\EB=NB[/tex]
we have
[tex]FE=6.1\ units\\FB=4.8\ units\\EB=3.8\ units[/tex]
therefore
[tex]BN=3.8\ units[/tex]
the answer is
the length of BN is [tex]3.8\ units[/tex]
Which description matches the algebraic expression 45n
A.the sum of a number and 45
B. the quotient of a number and 45
C. the product of a number and 45
D. the difference of a number and 45
Answer: The correct description is (C). the product of a number and 45.
Step-by-step explanation: We are given to select the correct description that matches the algebraic expression 45n.
Let, 'n' be a number.
Then, the sum of 'n' and 45 is written as (45 + n).
So, option (A) is incorrect.
The quotient of 'n' and 45 is given by [tex]\dfrac{n}{45}~\textup{or}~\dfrac{45}{n}.[/tex]
So, option (B) is incorrect.
The product of 'n' and 45 is
45 × n = 45n, which means 45 times of a number 'n' or n times of 45.
So, option (C) is correct.
The difference of 'n' and 45 is (n - 45) or (45 - n), according as 'n' is greater or 45 is greater.
So, option (D) is incorrect.
Thus, the correct option is (C).
if there are four people and two of the are zombies,then there are a 100 people how many are zombies
The following temperatures were recorded in Pasadena for a week in April: 87, 85, 80, 78, 83, 86, 90. Determine the interquartile range
What is the equation of a line perpendicular to the line 7x+4y=15+2x and passes through the point (0.5,0.5)?
Create an algebraic expression or equation that might model any of the behaviors you observe. Then, explain your reasoning.
Write the quadratic function with the following transformations: vertical shrink by 3, left 4, down 9.
Find -8 ÷ 1/2 =
a.1/16
b.16
c.-1/4
d. -4
Simplify the square root of 16x^6th power
what is the slope of the line (2,5) and 7,25)
If r^n=a, then which of the following are true statements? Check all that apply.
a. a^1/n=r b. a^r=n c. n sq a =r d. n^1/r=a
There are two containers of milk. There is twice as much milk in the first container as in the second. After using 2 gal. of milk from the second container and 3 gal. of milk from the first container, the second container had 4.5 times less milk than the first. How many gallons of milk were in both containers originally?
Answer:
4.8 gallons in the first container, 2.4 in the second container.
The equation y=-5.131x^2 31.821x-3.333 approximates the number of people standing in line to catch commuter train x hours after 5am what is the best estimate for the number of people in line at 9am
41 is the best estimate for the number of people in line at 9am
What is Equation?Two or more expressions with an Equal sign is called as Equation.
y equal to minus five point one three one x square plus Thirty one point eight two one x minus three point three three three.
y=-5.131x²+ 31.821x-3.333 approximates the number of people standing in line to catch commuter train x hours after 5am.
There is 4 hours in between 9 am and 5 am. so x=4
Substitute x=4 into the equation
y=-5.131(4)²+ 31.821(4)-3.333
y=-5.131(16)+127.284-3.333
y=-82.096+127.284-3.333
y=41.855
Hence 41 is the best estimate for the number of people in line at 9am
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Which of the following points are on the line given by the equation y=1/2x?
Check all that apply
A. (2, 1)
B. (3, 15)
C. (4, 2)
D. (3, 6)
E. (-2, 1)
F. (-2, -1)
Answer: (2,1) (4,2) (-2,-1)
Step-by-step explanation:
thats apex, my dude
Answer:
Option A, C, F are the correct options.
Step-by-step explanation:
The given equation of line is [tex]y=\frac{1}{2}x[/tex]
Now we will plug in the values of points and validate the equation.
Option A. (2, 1)
[tex]y=\frac{1}{2}x[/tex]
[tex]1=\frac{2}{2}=1[/tex]
So this points lies on the given equation of line.
Option B. (3, 15)
[tex]15\neq \frac{3}{2}[/tex]
So the point is not on the line.
Option C. (4, 2)
[tex]2=\frac{4}{2}=2[/tex]
Point lies on the line.
Option D. (3, 6)
[tex]6\neq \frac{3}{2}[/tex]
Therefore point is not on the line.
Option E. (-2, 1)
[tex]1\neq \frac{-2}{2}[/tex]
Point does not lie on the line.
Option F. (-2, -1)
[tex]-1=\frac{-2}{2}=-1[/tex]
So this point lies on the line.
There are three points (2, 1), (4, 2) and (-2, -1) are on the line.
What is the equation of the line that is perpendicular
The range of f(x) = |-x| is _____.
y < 0 , y > 0 , y ≤ 0 , y ≥ 0
Answer:
y ≥ 0
Step-by-step explanation:
The real absolute value function is defined on the set of all real numbers, assigning each real number its respective absolute value. Formally, the absolute value of any real number x, is defined by:
[tex]|x|=x,\hspace{3}if\hspace{3}x\geq0\\|x|=-x,\hspace{3}if\hspace{3}x<0[/tex]
The domain of the function is all real numbers, and by definition, the absolute value of x will always be greater than or equal to zero and never negative. Hence:
[tex]Domain:\\x\in R\\Range:\\y\in R : y\geq0[/tex]
I attached you a picture of the graph.
What does the greater than sign with the line under it mean?
Find two consecutive odd numbers such that the sum of the larger number and twice the smaller number is 27 less than four times the smaller number
What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?
Enter your answer in the box.
Answer:
[tex]\frac{2}{3}[/tex] is the Slope of a line that is perpendicular to a given line equation -2y=3x+7
Step-by-step explanation:
We are given here with the equation of the line [tex]-2y=3x+7[/tex] or we can write this equation as [tex]y=\frac{-3}{2}x+\frac{-7}{2}[/tex]
the general equation of the line [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
Compare the given equation with general equation we get,
the value of slope(m) [tex]=\frac{-3}{2}[/tex]
The slope of line perpendicular to a line is, [tex]m_{perpendicular}=\frac{-1}{m}[/tex]
Since, the slope of the given line is, m=[tex]\frac{-3}{2}[/tex]
then, [tex]m_{perpendicular}=\frac{-1}{\frac{-3}{2} }[/tex][tex]=\frac{2}{3}[/tex]
Therefore, the slope of a line that is perpendicular to a line whose equation is -2y=3x+7 is, [tex]\frac{2}{3}[/tex]
The slope of the line that is perpendicular to a line whose equation is -2y = 3x + 7 is 2/3.
For lines to be perpendicular to each other, the product of there slopes is equals to negative 1. This can be mathematically represented as follows
m₁ × m₂ = -1
where
m₁ and m₂ are slopes of the lines.
Therefore,
let's find the slope of the equation given
-2y = 3x + 7
divide both sides by -2
y = -3/2 x + 7/2
Using the slope equation model,
y = mx + c
where
m = slope
The slope in our equation will be - 3/2.
Using the first formula for perpendicular lines,
m₁ × m₂ = -1
-3/2 m₁= -1
m₁ = -2/-3
m₁ = 2/3
The slope of the line is 2/3
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