The area, to the nearst square inch, of a circle the same size az the bicycle wheel is 531 inches².
What is the area of the circle?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 22/7
R = radius
The full rotation of the wheel is equal to the circumference of the wheel.
circumference of the wheel = 2 πr
26π = 2 πr
r = 13 inches
Area = 22/7 x 13³ = 531 inches²
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Please help with these 2 questions and explain why it's the answer
First, let's edit the given equations.
In 9:[tex]2(32-x^2)=4x4-2\\\\64-2x^2=14[/tex]
Then, to check if [tex]x=5[/tex] is a solution to this equation, let's put the [tex]5[/tex].
[tex]64-2(5)^2=14\\\\64-50=14[/tex]
That's correct!
In 10:[tex]4^2-x\leq x(6-5)\\\\16-x\leq 6x-5x\\\\16-x\leq x\\\\16\leq 2x\\\\x\geq 8[/tex]
Then, we must put [tex]15[/tex].
[tex]15\geq 8[/tex]
That's correct!
Good luck! If you have any question(s), then feel free to ask in comments!
Hi Student!
Let us first look at what the first question is asking for us to do and what is provided to do that. Looking at the first question we see that they are asking if x = 5 is a solution to the expression that they provided. This type of problem is fairly simple and what we basically do is just plug in the value 5 for the variable x in the expression and the simplify both sides to see if they are the same.
Plug in the values
[tex]2(32 - x^2) = 4 * 4 - 2[/tex][tex]2(32 - (5)^2) = 4 * 4 - 2[/tex]Simplify the square and subtract inside of the parenthesis
[tex]2(32 - 25) = 4 * 4 - 2[/tex][tex]2(7) = 4 * 4 - 2[/tex]Simplify both sides
[tex]2 * 7 = (4 * 4) - 2[/tex][tex]14 = (16) - 2[/tex][tex]14 = 14[/tex]Looking at the final expression that we have, we can see that we have 14 is equal to 14 which is true and therefore x = 5 is a solution of the expression provided.
Moving onto the next question, we can see that it asks for us to do something really similar to the previous question but this time to check if x = 15 is a solution of a different expression. Let's follow the same steps that we did last time.
Plug in the values
[tex]4^2 - x \le x(6 - 5)[/tex][tex]4^2 - (15) \le 15(6 - 5)[/tex]Distribute the x
[tex]4^2 - (15) \le (15 * 6) + (15 * -5)[/tex][tex]4^2 - (15) \le 90 - 75[/tex]Simplify both sides
[tex]16 - 15 \le 90 - 75[/tex][tex]1 \le 15[/tex]Looking at the final expression that we have, we can see that it states that 1 is less than or equal to 15 and that is true. Therefore, x = 15 is a solution of the expression that was provided.
The high temperatures for the week of November 27- December 1 were 66 ℉, 7 1 ℉, 68 ℉, 70 ℉, and 65 ℉. What was the average high temperature (in ℉) for that week? Show your work.
Answer:
68 degrees Fahrenheit
Step-by-step explanation:
to find the average also known as mean, just add the numbers and divide by how many numbers there are.
66+71+68+70+65=340
Now, divide by how many numbers there are. There are 5.
So,
340÷5 = 68
the average is 68.
Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-half x minus three-halves?
f Superscript negative 1 Baseline (x) = one-half x minus three-halves
A function assigns the value of each element of one set to the other specific element of another set. The inverse of the function g(x)=-2x -3.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Two function are inverse of each other if,
f(g(x))=x
g(f(x)) = x
Since the function is inverse, therefore, we can write,
g(f(x)) = a(-1x/2 - 3/2) + b
x = -ax/2 - 3x/2 + b
-a/2 = 1
a = -2
-3a/2 + b = 0
b= -3
Thus, the inverse of the function g(x)=-2x -3.
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Answer:
the inverse of the function g(x)=-2x +3 .
Step-by-step explanation:
An icicle drips at a rate that can be represented by the function f(x) = −x2 + 8x − 7, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. When f(x) is a negative number, the icicle is not dripping. Determine the values when the icicle starts and stops dripping.
Find when f(x) = 0. By factorizing, we have
-x² + 8x - 7 = - (x - 7) (x - 1) = 0
so either x - 7 = 0 or x - 1 = 0, or simply x = 1 or x = 7.
Split the domain into three intervals, and check the sign of f(x) over each interval at some test point in the interval. The sign will tell you when the icicle is dripping (positive) or not (negative).
• [0, 1) : at x = 0, we have f(0) = -7 < 0
• (1, 7) : at x = 2, we have f(2) = 5 > 0
• (7, 10] : at x = 8, we have f(8) = -7 < 0
This tells us that the icicle is not dripping when 0 ≤ x < 1, begins to drip when x = 1, drips for the duration of 1 < x < 7, stops dripping when x = 7, and keeps on not dripping when 7 < x ≤ 10.
A man travelled by train and left Nsawam at 10:43am and got at Dzorwulu at 3:23pm.Find the average speed of the train in km/hr if the distance of the journey was 356,140km.
Find the remainder when x4 - 5x3 + x2 - 10x - 5 is divided by x + 3.
Use the remainder theorem: we can decompose the given polynomial in terms of quotient and remainder polynomials [tex]q(x)[/tex] and [tex]r(x)[/tex], respectively, such that
[tex]x^4 - 5x^3 + x^2 - 10x - 5 = (x + 3) q(x) + r(x)[/tex]
Then letting x = -3 makes the quotient term vanish, and we're left with a remainder of
[tex]r(-3) = (-3)^4 - 5\times(-3)^4 + (-3)^2 - 10\times(-3) - 5 = \boxed{250}[/tex]
How is the graph of the parent function of y = RootIndex 3 StartRoot 0.5 x EndRoot transformed to produce the graph y = RootIndex 3 StartRoot x EndRoot?
It is horizontally stretched by a factor of mc031-3.
It is vertically stretched by a factor of mc031
It is translated left by mc031-5unit.
It is translated right by mc031-6.unit.
If any constant is added in the variable of the function. Then the function will shift towards left. Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The functions are given below.
y = ∛(0.5 + x)
y = ∛x
If any constant is added in the variable of the function. Then the function will shift towards left.
Then the correct option is C.
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Answer:
Step-by-step explanation:
The statement describe g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function is option C; Translate the parent function 5 units down and 7 units to the right.
How does transformation of a function happens?
The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
The transformed function can be written as
y = ∛(x - 5) + 7
Where f(x) = ∛x, this is of the form
y = ∛(x - 5) + 7
These numbers in these places correspond to ...
The statement describe g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function is option C; Translate the parent function 5 units down and 7 units to the right.
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Help please asap aaaaaaaaaaaaaaaaaa
Answer:
Step-by-step explanation:
Your exponential formula is in the form y = ab^x. In this form, the coefficient 'a' is the initial value, the y-intercept, the value when x=0. The value 'b' is the growth factor, which is 1 more than the growth rate per increment of x. This problem is asking for the growth rate to be expressed as a percentage.
__
Given p(x) = 78500(1.02^x), we can compare to the exponential function form to see that ...
a = 78,500b = 1.02 = 1 +0.02 = 1 +2%The value of x is zero in the year 2000, so the population that year is ...
p(0) = a = 78,500
The increase per year is the value of 'b' with 1 subtracted:
growth rate = 2% per year
st: Two- and Three-Dimensional Geometry
A solid machine part is to be manufactured as shown in the figure. The part is made by cutting a small cone off the top of a larger cone. The
small cone has a base radius of 3 inches and a height of 5 inches. The larger cone has a base radius of 9 inches and had a height of 15 inches
prior to being cut. What is the volume of the resulting part illustrated in the figure?
George and Maria decided to create a garden in their backyard. George works on the garden every third day and Maria works on the garden every fourth day.
If they worked on the garden today, the number of days until they work on the same day again would be.
Factor by grouping
5y^3(y-2)-15y(y-2)
5y³(y-2)-15y(y-2)
= (y-2)×(5y³-15y)
what is a variable in mathematics?
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Step-by-step explanation:
In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.
19% of what number is $6.46?
Answer:
here's the answer
Step-by-step explanation:
19/100*x=6.46
x=$34
If the given figure is sliced through points J. K. and L, which best describes the shape of the resulting cross-section?
A
OA parallelogram
OB. trapezoid
OC. rectangle
OD. triangle
The shape of the resulting cross-section will be equal to the trapezoid.
What is a trapezoid?A trapezoid is a quadrilateral having four sides whose two sides are parallel to each other and the other two sides are nonparallel to each other.
As it is given in the question the figure is sliced through points J. K. and When the shape is sliced from the given points it will create the trapezoidal shape that will have two parallel sides and the other two sides are Non-parallel
Therefore the shape of the resulting cross-section will be equal to the trapezoid.
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Answer:
Trapezoid
Step-by-step explanation:
I got it right on Edmentum
Hook me up with a 5 star and a thanks :)
The monthly rents for five apartments advertised in a newspaper were $650, $650, $800, $1900, and $820. Use the mean, median, and mode of the rents to answer the question. Which value best describes the monthly rents?
Answer:
The Median Best Describes The Monthly Rents
the mean is add up all the numbers and then divide by the amount of numbers so it is 4820 then divide by 5 = 964 so the mean of all of then is 964
the median you have to put it in slamets to biggest so 650 650 800 820 1900 and then you have to put the one(s) in the middle witch is 800 so the median is 800
the mode is the most common numbers that show up and there is 2 650 and one of everything else so the mode is 650
Hope This Helped
There is a rack of 11 billiards balls, numbered from 1 to 11. If one ball is selected at random, determine the odds in favor of it being at an even-number ball.
Answer:
5/11 odds / 45.45% chance of being even-numbered
Step-by-step explanation:
There are 5 even-numbered balls (2, 4, 6, 8, 10) and 6 odd-numbered balls (1, 3, 5, 7, 9, 11). So, 5 / 11 balls are even-numbered
if a ball is selected, it has a chance of 5/11 for being even-numbered
5/11 also = 45.45 % [rounded] chance of being even-numbered
which one is the answer
Answer:
hmmm I get 216
Step-by-step explanation:
(10×7)+(6×8) the front n back triangle +(6×7)+(8×7)
Please answer this problem!
Answer:
a. volume= 784 is the answer
−13x + 2/5 − 3 (2x + 4)
Write the equation that models the height of the roller coaster
Considering the circle described, the height of the roller coaster is modeled by the following equation:
[tex]y = \sqrt{900 - x^2}[/tex]
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, the roller coaster is represented by a circle centered at the origin, with radius 30, hence:
[tex]x^2 + y^2 = 30^2[/tex]
[tex]x^2 + y^2 = 900[/tex]
The height is the value of y, hence, considering it is a positive value:
[tex]y^2 = 900 - x^2[/tex]
[tex]y = \sqrt{900 - x^2}[/tex]
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consider the exponential functions below.
put the functions, with their corresponding intervals, in order from least to greatest according to their average rates of change over those intervals.
The functions in order from least to greatest according to their average rates of change are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]
How to order the functions?The rate of change is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
For function g at the interval [2,3], we have:
[tex]m = \frac{g(3) - g(2)}{3- 2}[/tex]
This gives
[tex]m = \frac{20 - 4}{3- 2}[/tex]
[tex]m =16[/tex]
For function h at the interval [0,2], we have:
[tex]m = \frac{h(2) - h(0)}{2- 0}[/tex]
Where:
h(2) = 3(3)^2 - 9 = 18
h(0) = 3(3)^0 - 9 = -6
This gives
[tex]m = \frac{18 + 6}{2 - 0}[/tex]
[tex]m = 12[/tex]
For function f at the interval [1,2], we have:
[tex]m = \frac{f(2) - f(1)}{2- 1}[/tex]
This gives
[tex]m = \frac{12 - 6}{2 - 1}[/tex]
[tex]m = 6[/tex]
Hence, the functions are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]
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I need help please ?!!!!
Answer:
6,010 mg
Step-by-step explanation:
1 gram = 1,000 milligrams that means
(6+.01)*1000=6,010mg
Help please!!!
A school building has a 100-foot guy wire attached to the top of the building. When pulled taut it touches level ground 42 feet from the base of the school. At approximately what angle does the wire make with the ground? Give the answer in degrees.
A) 24.83° B) 65.17° C) 22.78° D) 42° E) None of these
Answer: E) None of these
As you can see in the picture below, the line falls at around 66 degrees, so it can't be any of the given choices. If this answer turns out to be wrong, then it is probably B.
Hope this helps!
F(1) =3 and f (n+1)= f(n)^2+3 then find the value of f(4)
Answer:
f(4) = 1612
Step-by-step explanation:
using the recursive formula and f(1) = 3 , then
f(2) = f(1)² + 3 = 3² + 3 = 9 + 3 = 12
f(3) = f(2)² + 3 = 144 + 3 = 147
f(4) = f(3)² + 3 = 147² + 3 = 1609 + 3 = 1612
Which coordinate point is a solution to the linear equation? (The graph counts by 1s)
Answer:
the point through which it passes i.e (1,5)
Answer:
(1,5)
Step-by-step explanation:
All points on the line is solution of the equation.
(1 ,5) is on the line and so it is the solution
If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days, what is the amountof her deposit to the
nearest dollar (zero decimal place). Use a 360-day year
The amount of Rita deposit is $2556.
What is Simple Interest ?The interest calculated on the principal amount or the initial investment.
It is given in the question
If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days.
P = ?
S.I. = $63.90
Interest = 6%
T = 150days
S.I. = (P *R*T)/100
63.90 = P * 6 * 150*100 /360
63.90 * 360*100 /( 150 *6) = P
P = $2556
Therefore the amount of Rita deposit is $2556.
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Figure the amount of concrete (in cubic yards) required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′. Show both exact and rounded figures in the blanks provided
The amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.
What is a Cuboid ?A cuboid is a three dimensional shape , with 6 faces , each face is a rectangle.
The concrete can be considered as in the shape of a cuboid.
Length = 18
Breadth = 24'
Height = 4"
Volume of Cuboid = Length * Breadth * Height
Volume of the cuboid = 18 * 24 * 4 *12*12 *(0.0278)³
=5.34 cu.yard.
Therefore the amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.
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Type the correct answer in the box. Rewrite the quadratic function in the form that best reveals the zeros of the function. f(x)=2(2x2+4x)+3
Try this suggested option:
Step-by-step explanation:
f(x)=2(2x²+4x)+3; ⇔
f(x)=4(x²+2x)+3; ⇔
f(x)=4(x²+2x+1)+3-4; ⇔
f(x)=4(x+1)²-1; ⇔
f(x)=(2x+1)(2x+3).
Then the roots are:
[tex]\left[\begin{array}{ccc}x=-1.5\\x=-0.5\end{array}.[/tex]
the diagram below shows the use of diverging lens for correction of
Answer:
E
Step-by-step explanation:
The diagram below shows the correct use of diverging lens for correction of myopia.
help me solve this pls
Answer:
B.) f(x) = |x| , g(x) = 9x + 2
Step-by-step explanation:
The expression f о g = H is identical to f(g(x)) = H. In other words, when you put the function g(x) in the "x" position of the f(x) function, it should look like the H(x) function.
If g(x) = 9x + 2, put the entire function in for "x" in f(x) = |x|. Once you do this, you get the function f(g(x)) = |9x + 2|.
Answer:B.) f(x) = |x| , g(x) = 9x + 2
Step-by-step explanation:
The expression f о g = H is identical to f(g(x)) = H. In other words, when you put the function g(x) in the "x" position of the f(x) function, it should look like the H(x) function.
If g(x) = 9x + 2, put the entire function in for "x" in f(x) = |x|. Once you do this, you get the function f(g(x)) = |9x + 2|.