Answer:
22.5 feetStep-by-step explanation:
The formula for circumference is 2(3.14)r
So, we divide 141.3 by 6.28 and get 22.5
The radius is 22.5 feet.
What value of m satisfies the equation
m-2=2-m?
Answer:
m = 2
Step-by-step explanation:
m - 2 = 2 - m
2m = 4
m = 2
Hello,
Answer: m = 2
Step-by-step explanation:
m - 2 = 2 - m
⇔ m - 2 + m = 2 - m + m
⇔ 2m - 2 = 2
⇔ 2m - 2 + 2 = 2 + 2
⇔ 2m = 4
⇔ 2m/2 = 4/2
⇔ m = 2
Draw the image of the figure under the given rotation. Triangle PQR; 90 degrees about the the origin. Number 2 :)
The attached figure represents the image of the triangle under the rotation
How to draw the image of the triangle?The coordinates of the triangle are given as:
P = (2, 1)
Q = (4, 1)
R = (4, -3)
The rule of 90 degrees rotation about the origin is:
(x, y) = (y, -x).
So, we have:
P' = (1, -2)
Q' = (1, -4)
R' = (-3, -4)
See attachment for the figure under the rotation
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Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.
f(x)=
x+a
b
g(x)=cx−d
Part 2. Show your work to prove that the inverse of f(x) is g(x).
Part 3. Show your work to evaluate g(f(x)).
Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y = x on the same graph.
Task 2
Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model:
a√x+b+c=d
Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation.
Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.
Part 3. Explain why the first equation has an extraneous solution and the second does not.
See below for the solution to the inverse function and the rational equation
The function and the inverseCreate functions f(x) and g(x)
The functions are given as:
f(x) = x + a/b
g(x) = cx − d
Let a = 4 and b = 2.
So, we have:
f(x) = x + 4/2
Rewrite as:
y = x + 2
Swap x and y
x = y + 2
Make y the subject
y = x - 2
So, we have:
g(x) = x - 2
So, the functions are:
f(x) = x + a/b ⇒ f(x) = x + 4/2
g(x) = cx − d ⇒ g(x) = x - 2
Show that the functions are inverse functions
In (a), we have:
f(x) = x + 4/2
g(x)= x - 2
If the functions are inverse functions, then:
f(g(x)) = x
We have:
f(x) = x + 4/2
This gives
f(g(x)) = g(x) + 4/2
This gives
f(g(x)) = x - 2 + 4/2
Evaluate
f(g(x)) = x
Evaluate g(f(x))
In (a), we have:
f(x) = x + 4/2
g(x)= x - 2
We have:
g(x)= x - 2
This gives
g(f(x)) = f(x) - 2
This gives
g(f(x)) = x + 4/2 - 2
Evaluate
g(f(x)) = x
Graph the functions
See attachment for the graph
The table of values is:
x f(x) g(x)
0 2 -2
1 3 -1
2 4 0
3 5 1
4 6 2
Radical equationsCreate the equations
The form of the equations is given as:
[tex]a\sqrt{x + b} + c= d[/tex]
So, we have:
[tex]\sqrt{4x + 5} + 1 = 0[/tex] --- has extraneous solution
[tex]2\sqrt{3x - 1} + 2 = 8[/tex] --- has no extraneous solution
The equation solution
Equation 1 with extraneous solution
[tex]\sqrt{4x + 5} + 1 = 0[/tex]
Subtract 1 from both sides
[tex]\sqrt{4x + 5} = -1[/tex]
Square both sides
4x + 5 = 1
Evaluate the like terms
4x = -4
Divide by 4
x = -1
Substitute x = -1 in [tex]\sqrt{4x + 5} + 1 = 0[/tex] to check
[tex]\sqrt{4(-1) + 5} + 1 = 0[/tex]
[tex]\sqrt{-4 + 5} + 1 = 0[/tex]
[tex]\sqrt{1} + 1 = 0[/tex]
Evaluate the root
[tex]1 + 1 = 0[/tex]
[tex]2= 0[/tex] --- false
Equation 2 without extraneous solution
[tex]2\sqrt{3x - 1} + 2 = 8[/tex]
Subtract 2 from both sides
[tex]2\sqrt{3x - 1} = 6[/tex]
Divide by 2
[tex]\sqrt{3x - 1} = 3[/tex]
Square both sides
3x - 1 = 9
Evaluate the like terms
3x = 10
Divide by 3
x = 10/3
Substitute x = x = 10/3 in [tex]2\sqrt{3x - 1} + 2 = 8[/tex] to check
[tex]2\sqrt{3 * \frac{10}{3} - 1} + 2 = 8[/tex]
[tex]2\sqrt{10 - 1} + 2 = 8[/tex]
[tex]2\sqrt{9} + 2 = 8[/tex]
Evaluate the root
[tex]2*3 + 2 = 8[/tex]
[tex]8 = 8[/tex] --- true
Why the equations have (or do not have) an extraneous solution
The first equation has an extraneous solution because the solution is false for the original equation and the second does not have an extraneous solution because the solution is true for the original equation
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help me please please please!!!
What formula should be used to calculate an unknown side of a right angled triangle
when the hypotenuse (c) and one other side (b) are known?
a) Oa^2 = b^2-c^2
b) Oa^2 = c^2 + b^2
c) Oa^2 = c^2-b^2
d) Oc^2 = a^2 - b^2
e) Oc^2 = b^2- a^2
Answer:
c) Oa^2 = c^2-b^2
Step-by-step explanation:
the formula of finding hypotenuse (c) is
c^2 = a^2 + b^2
that means c^2 - b^2 = a^2
a^2 = c^2 - b^2.
Today is march 28 in 6 weeks and 1 day the freshmen class of 2025 will be going on to a carnival staycation what is the date on their field trip
why do angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle ?
Because the lines drawn are straight.
Explanation:
When the straight lines join together, the original point from where the first line started, becomes a right angle (90°)
Help please!
A vocational school admits 4 out of every
10 people who apply for admission. One
year, 640 students were admitted. How
many people applied for admission?
Answer:
319
Step-by-step explanation:
i am really not sure but i believe so i hope it is the right answer
Answer:
1600 people
Step-by-step explanation:
This is a ratio problem. We can set up the proportion by letting x be the number of people who applied for admission:
[tex]\frac{4}{10}=\frac{640}{x}[/tex]
Since we know that 4 people get in for every 10 people that apply, we can set up an equation like the one above and solve for x by cross multiplying:
[tex]6400=4x\\x=1600[/tex]
This means that 1600 people applied for admission to the vocational school.
I’m what quadrant does theta lie if the following statements are true? Sec(theta)<0 and (sec (theta) )(csc (theta) ) > 0
Because the cosine and sine must be negative when evaluated in theta, the angle lies on the third quadrant.
In which quadrant is the endpoint of the segment that defines the angle?We know that if:
cos(θ) > 0, then we are on the first or fourth quadrantsin(θ) > 0, then we are on first or second quadrant.Here we know that:
sec(θ) < 0
And we know that:
sec(θ) = 1/cos(θ)
Then we have cos(θ) < 0
We also have that:
sec(θ)*csc(θ) > 0
Because sec(θ) < 0, we must have that csc(θ) < 0.
Remember: csc(θ) = 1/sen(θ)
Then sen(θ) < 0.
Then we have the two conditions:
sen(θ) < 0
cos(θ) < 0
The cosine is negative on the third and second quadrants.The sine is negative on the third and fourth quadrants.The only quadrant where both are negative is the third quadrant, so that is the correct option.
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Suppose Z has a standard normal distribution with a mean of 0 and a standard deviation of 1. 27% of the possible Z values are smaller than __________.
Suppose Z has a standard normal distribution with a mean of 0 and a standard deviation of 1. 27% of the possible Z values are smaller than 0.613.
The standard normal distribution, also known as the z-distribution, is a special normal distribution with a mean of 0 and a standard deviation of 1. The normal distribution can be standardized by converting its value to a z-score. The Z-score indicates how many standard deviations each value has from the mean.
The standard normal distribution (z distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. Each point (x) of the normal distribution can be converted to the standard normal distribution (z) using the equation z = (x-mean) / standard deviation.
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anybody can help me?
The proportional graph that corresponds to M = 3n is: Graph C.
What is a Proportional Graph?The constant of proportionality, k, of a proportional graph is given as, y/x. The graph is expressed by the equation, y = kx.
The equation given, M = 3n, represents a proportional relationship where k = 3.
Using a point on graph C, (400, 1,200):
k = 1,200/400
k = 3
Therefore, the graph that corresponds to the situation is: C.
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If the probability of observing at least one car on a highway during any 20-minute time interval is 609/625, then what is the probability of observing at least one car during any 5-minute time interval
If the probability of observing at least one car on a highway during any 20-minute time interval is 609/625, then the probability of observing at least one car during any 5-minute time interval is 609/2500
Given The probability of observing at least one car on a highway during any 20 minute time interval is 609/625.
We have to find the probability of observing at least one car during any 5 minute time interval.
Probability is the likeliness of happening an event among all the events possible. It is calculated as number/ total number. Its value lies between 0 and 1.
Probability during 20 minutes interval=609/625
Probability during 1 minute interval=609/625*20
=609/12500
Probability during 5 minute interval=(609/12500)*5
=609/2500
Hence the probability of observing at least one car during any 5 minute time interval is 609/2500.
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Solve for all of the missing angles in the rhombus below, given that m∠3 = 54°. (Round to the nearest tenth as needed.)
The measure of angles 1, 2, 4, and 5 are 54 degrees, 90 degrees, 36 degrees, and angle 36 degrees.
What is a rhombus?A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.
We have shown the rhombus in the picture.
As we know the diagonals bisect at a 90-degree angle.
So angle 2 = 90 degree
angle 1 = angle 3
angle 1 = 54 degrees
angle 1 + angle 2 + angle 5 = 180
54 + 90 + angle 5 = 180
angle 5 = 36 degrees
angle 5 = angle 4 = 36 degrees
Thus, the measure of angles 1, 2, 4, and 5 are 54 degrees, 90 degrees, 36 degrees, and angle 36 degrees.
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PLS QUICK I ONLY HAVE 2 HOURS
Answer:
D
Step-by-step explanation:
As you can observe from the pattern, the numerator gets multiplied by 4 every increase in the sequence.
So , clearly, the 5th term will be = [tex]\frac{64*4}{5} =\frac{256}{5}[/tex]
and the 6th term will be = [tex]\frac{256*4}{5} =\frac{1024}{5}[/tex]
Therefore , D will be the answer.
A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 2 cm and standard deviation 0.1 cm. The specifications call for corks with diameters between 1.9 and 2.1 cm. A cork not meeting the specifications is considered defective. (A cork that is too small leaks and causes the wine to deteriorate; a cork that is too large doesn't fit in the bottle.) What proportion of corks produced by this machine are defective
The proportion of defective corks produced by this machine through z test comes out is 0.320.
Given mean of 2 cm and standard deviation of 0.1 cm, The diameter is between 1.9 and 2.1 cm.
We have to find the proportion of defective corks that are produced by machine.
In this problem we have to first find z score and then we will be able to find the probability of defective corks produced by the machine.
Z=(X-μ)/σ
μ=2 cm and σ=0.1 cm.
Z value corresponding to X=1.9.
Z=(1.9-2)/0.1
=-0.1/0.1
=-1
Z value corresponding to X=2.1.
Z=(2.1-2)/0.1
=0.1/0.1
=1
P value of P(-1<Z<1)=2*0.3410=0.6820
Proportion of corks which are not defective=0.6820.
Proportion of corks which are defective=1-0.680.
=0.320
Hence the proportion of defective corks produced by machine is 0.320.
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Which of the following is the difference of two squares? (Answers below)
Answer:
c and d, because they both have 2 squares
Sarita makes a conical hat out of stiff felt. She packs the hat into the box so that the edge of the base just touches all four edges of the box and the tip of the hat touches the top of the box. The box is a rectangular prism that is 16 by 16 by 15 centimeters. How much material was used to create the hat? Round to the nearest tenth of a square centimeter
The material needed to make the hat is 3840 cm³.
How to find the volume of a rectangular prism?The hat occupies the whole volume of the rectangular box. Therefore, the material needed to make the hat is the volume of the rectangular box it occupies.
Therefore,
volume of a rectangular prism = lwh
where
l =lengthw = widthh = heightTherefore,
l = 16 cm
w = 16 cm
h = 15 cm
volume of a rectangular prism = 16 × 15 × 16
volume of a rectangular prism = 3840 cm³
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A triangle is translated by using the rule (x,y) (x-4,y+2) which describes how the figure is moved ?
Answer:
4 units to the left and 2 units up.
Step-by-step explanation:
Mrs. Ibarra wants to create a right triangle for a geometry test. She plans to use 15, 36, and 41 as side lengths.
Select the four true statements regarding the side lengths Mrs. Ibarra chose.
15 + 36 greater-than 41, so the side lengths will form a triangle.
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
Answer:
See below.
Step-by-step explanation:
Sides: 15, 36, 41
True: 15 + 36 greater-than 41, so the side lengths will form a triangle.
True: 15 squared + 36 squared = 1,521
True: 41 squared = 1,681
True: Since a squared + b squared not-equals c squared, it will not be a right triangle.
Answer:
A) 15 + 36 greater-than 41, so the side lengths will form a triangle.
C) 15 squared + 36 squared = 1,521
D) 41 squared = 1,681
E) Since a squared + b squared not-equals c squared, it will not be a right triangle.
Proof:
is x/3 = 5/6, then x =
A construction company prepares an
estimate to install a new pool for a home-
owner. The estimate includes h hours of
labor, where h>80. The company's goal
is for the estimate to be within 8 hours
of the actual number of hours of labor. If
the company meets the goal and it takes
a hours of actual labor, which inequality
represents the relationship between the
estimated number of hours of labor and
the actual number of hours of labor?
A) a+h≤8
B) a2h+8
C) ash-8
D) -8≤a-h≤8
The equation that represents the relationship between the estimated number of hours of labor and the actual number of hours of labor is D. -8≤a-h≤8.
How to illustrate the equation?From the information given, the estimate includes h hours of labor, where h>80 and the company's goal is for the estimate to be within 8 hours of the actual number of hours of labor.
Here, the equation that represents the relationship between the estimated number of hours of labor and the actual number of hours of labor is -8≤a-h≤8.
In conclusion, the correct option is D.
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In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS?
QS = 13
5 < QS < 8
QS > 13
3 < QS < 13
The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The length of QS can lie between 3 < QS < 13.
What is the triangle inequality theorem?The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
(a+b) > c(b+c) > a(c+a) > bAs per the given law of triangle inequality, the sum of the two sides of the triangle is greater than the third side.
x + 8 > 5
x > -3
x + 5 > 8
x > 3
8 + 5 > x
13 > x
Hence, the length of QS can lie between 3 < QS < 13.
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Write an equation in slope-intercept form of the line containing the points (3,-1) and (6, 7).
=x-9
y=x-7
y = -x +9
y = 3x - 11
The equation in slope-intercept form of the line containing the points (3,-1) and (6, 7) is; y = ⁸/₃x - 7
What is the equation in Slope Intercept form?We are given the coordinates of two points as;
(3,-1) and (6, 7).
Now, the formula for the equation of the line containing the two points in slope intercept form is;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
Thus, we have;
(y + 1)/(x - 3) = (7 + 1)/(6 - 3)
(y + 1)/(x - 3) = = 8/3
y + 1 = (8/3)(x - 3)
y + 1 = ⁸/₃x - 8
y = ⁸/₃x - 7
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number 8. use the Steps in the construction to determine which statement is true
Answer:
I believe the answer is C
Step-by-step explanation:
Hope this helps!!!
Desarrollar por el metodo de reduccion: 1. si: { 3x+ 2y = 26 { 5x - y = 26 hallar: e= x +y
Answer: e= x + y = 10
Step-by-step explanation :
check out the attachment for the answer
We got the value of [tex]e=\frac{78}{7}[/tex] by solving the given equations [tex]3x+2y=26[/tex] and [tex]5x+y=26[/tex] by reduction method.
What is reduction method?The reduction or elimination approach includes using arithmetic operations between equations to produce equivalent equations with fewer unknowns that are simpler to analyze and evaluate.
Given equations are
[tex]3x+2y=26[/tex] .........(1)
[tex]5x+y=26[/tex] ...........(2)
We need to find the value of [tex]e=x+y[/tex]
Simplifying the given equation (2) and we get
[tex]5x+y=26\\\Rightarrow y=26-5x[/tex]................(3)
Now, substitute the equation (3) in equation (1) and we get
[tex]3x+2(26-5x)=26\\\Rightarrow 3x+52-10x=26\\\Rightarrow -7x+52=26\\\Rightarrow -7x=26-52\\\Rightarrow -7x=-26\\\Rightarrow x=\frac{26}{7}[/tex]
Substitute the value of x in equation (3), we get
[tex]y=26-5\frac{26}{7} \\\Rightarrow y=26-\frac{110}{7}\\\Rightarrow y=\frac{162-110}{7}\\\Rightarrow y=\frac{52}{7}\\[/tex]
Now adding the values of x and y, we get
[tex]\therefore e=\frac{26}{7}+\frac{52}{7}\\\Rightarrow e=-{[\frac{26+52}{7}]\\\Rightarrow e={[\frac{78}{7}][/tex]
Therefore, the value of [tex]e=\frac{78}{7}[/tex].
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The boarding platform of a Ferris wheel is 2 meters above the ground and the Ferris wheel is 36 meters in diameter and spins once every 7 minutes. How many minutes of the ride are spent higher than 26 meters above the ground
what is the area of the shaded region?
To find the area of composite shapes, we can break the bigger shape down into small, simpler shapes, and find the sum of their areas.
For this triangle, we will need to know the formula to find the area of a triangle:
[tex]A=\dfrac{1}{2}bh[/tex]
Solving the QuestionThe given shape can be seen as one large triangle with a little triangle cut out of it. To find the shaded region, we can:
Find the area of the large triangleFind the area of the little triangleSubtract the area of the little triangle from the large triangleArea of the Large Triangle[tex]A=\dfrac{1}{2}bh[/tex]
⇒ Plug in the values given for the base and height:
[tex]A=\dfrac{1}{2}(5)(2+4+6)\\\\A=\dfrac{1}{2}(5)(12)\\\\A=(5)(6)\\\\A=30 mm^2[/tex]
Area of the Small Triangle[tex]A=\dfrac{1}{2}bh[/tex]
⇒ Plug in the values given for the base and height:
[tex]A=\dfrac{1}{2}(3)(4)\\\\A=(3)(2)\\\\A=6mm^2[/tex]
Subtract the Area of the Small Triangle from the Area of the Large Triangle[tex]30 mm^2-6mm^2\\=24mm^2[/tex]
AnswerThe area of the shaded region is [tex]24mm^2[/tex].
The graph of f(x) consists of 14 points. Six of the points lie in Quadrant I of the coordinate plane. If f(x) is an odd function,
what is the greatest number of points that can lie in Quadrant II?
O one
O two
O six
O eight
If f(x) is an odd function, the greatest number of points that can lie in Quadrant II is 1
How to determine the number of points?The given parameters are:
Function f(x) = Odd function
Points in quadrant IV
The number of points in the upper quadrants is:
Upper = 14/2
This gives
Upper = 7
The upper quadrants are I and II
This means that:
I + II = 7
So, we have:
6 + II = 7
Subtract 6 from both sides
II = 1
Hence, the greatest number of points that can lie in Quadrant II is 1
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You should be able to find this
without a calculator.
cos(cos-¹ 0.3) = [?]
Hello:
Let's consider this problem in steps:
Let's gather some information:
cosine and arccosine cancel each other out in this caseNow let's apply our knowledge to solve the problem:
[tex]\rm \hookrightarrow cos(cos^{-1}0.3) = 0.3[/tex]
Answer: 0.3
Hopefully that helps!
[tex]\frak{Hi!}[/tex]
[tex]\large\text{Related Concept-:}[/tex]
[tex]\boxed{\begin{minipage}{10cm} \sf{If\;you\;take\;the\;inverse\;cosine}\\ \;of\;a\;number,\;and\;then\;take\; its\;cosine,\;don't\;you\;get\;the\;number \\ you started with? \end{minipage}}[/tex]
ClarificationThe inverse cosine and the cosine are operations that undo each other.
This being said, let's solve our problem.
[tex]\bf{cos(cos^{-1}\;0.3)=0.3[/tex], based on what I said above
[tex]\cal{CALLIGRAPHY}[/tex]
Write the domain and range of g using interval notation.
The domain is (-2, 3) and the range is (-3, 4]
How to determine the domain and the range?The domain
This is the possible x values
From the graph, we have the following highlights:
Minimum x = -2Maximum x = 3The endpoints at these intervals is a open circle
Hence, the domain is (-2, 3)
The range
This is the possible y values
From the graph, we have the following highlights:
Minimum y = -3Maximum y = 5The endpoint at the minimum is a open circle, while the maximum is a closed circle
Hence, the range is (-3, 4]
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SATQuestion:
The scatterplot below shows the amount of electric energy generated, in millions of megawatt hours, by nuclear sources over a 10-year period.
\bigstar★ Scatterplot in the attachment....
Of the following equations, which best models the data in the scatterplot?
A) y = 1.674x² + 19.76x - 745.73
B) y = -1674x2 - 19.76x - 745.73
C) y = 1.674x² + 19.76x + 745.73
D) y = -16743+ 19.76x + 745.73
Please answer with proper explanation and workout. Spam, Vulgar and short answers will be deleted at the spot✓.
The equation which best models the data in the scatterplot is: D. y = -16743x² + 19.76x + 745.73.
How to interpret the scatter plot?By critically observing the scatter plot shown in the image attached below, we can logically deduce that it's data are best modelled by a quadratic equation (parabolic curve).
Mathematically, the equation of a quadratic equation (parabolic curve) is given by:
y = ax² + bx + c
Since the parabolic curve opens downward, we have:
a < 0, c > 0, x = 0 and y > 0;
y = -16743x² + 19.76x + 745.73.
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