Answer:
A rational number is a number that can be expressed as a fraction (the ratio of two integers).
Integer: A whole number that can be positive, negative, or zero.
To calculate if each radical can be expressed as a rational number, convert the decimals into rational numbers, then simplify:
[tex]\sqrt{121}=\sqrt{11^2}=11=\dfrac{11}{1} \quad \leftarrow \textsf{rational}[/tex]
[tex]\sqrt{12.1}=\sqrt{\dfrac{1210}{100}}=\dfrac{\sqrt{1210}}{\sqrt{100}}=\dfrac{\sqrt{121\cdot 10}}{10}=\dfrac{\sqrt{121}\sqrt{10}}{10}=\dfrac{11\sqrt{10}}{10} \leftarrow \textsf{not rational}[/tex]
[tex]\sqrt{1.21}=\sqrt{\dfrac{121}{100}}=\dfrac{\sqrt{121}}{\sqrt{100}}=\dfrac{\sqrt{11^2}}{\sqrt{10^2}}=\dfrac{11}{10} \leftarrow \textsf{rational}[/tex]
[tex]\sqrt{0.0121}=\sqrt{\dfrac{121}{10000}}=\dfrac{\sqrt{121}}{\sqrt{10000}}=\dfrac{\sqrt{11^2}}{\sqrt{100^2}}=\dfrac{11}{100} \leftarrow \textsf{rational}[/tex]
Therefore, [tex]\sf \sqrt{12.1}[/tex] is not a rational number.
Someone help me with this
Answer:
radius = √35 mm or 5.916 mm
Explanation:
[tex]\sf area \ of \ circle = \pi r^2[/tex]Here:
area of circle: 110 mm²π taken as 22/7Solve for radius:
[tex]\rightarrow \sf \pi r^2 = 110[/tex]
[tex]\rightarrow \sf \dfrac{22}{7} r^2 = 110[/tex]
[tex]\rightarrow \sf r^2 = \dfrac{110(7)}{22} =35[/tex]
[tex]\rightarrow \sf r = \sqrt{35}[/tex]
Let's see
Area=110πr²=11022/7r²=110r²≈110(7)/22r²=770/22r=√770/22r=5.9mmPLEASE HELP ME I'M GIVING 20PTS AND MARKING BRAINLIEST!!!!
If sinθ=1/3, what are the values of cosθ and tanθ?
Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:
[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex][tex]\tan{\theta} = \pm \frac{\sqrt{2}}{4}[/tex]What is the trigonometric identity using in this problem?The identity that relates the sine squared and the cosine squared of the angle, as follows:
[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]
In this problem, we have that the sine is given by:
[tex]\sin{\theta} = \frac{1}{3}[/tex]
Hence, applying the identity, the cosine is given as follows:
[tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex]
[tex]\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2[/tex]
[tex]\cos^2{\theta} = 1 - \frac{1}{9}[/tex]
[tex]\cos^2{\theta} = \frac{8}{9}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{8}{9}}[/tex]
[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex]
The tangent is given by the sine divided by the cosine, hence:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]
[tex]\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}[/tex]
[tex]\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\tan{\theta} = \pm \frac{\sqrt{2}}{4}[/tex]
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Is ab parallel to cd? explain.
yes, because both lines have a slope of 4/3.
yes, because both lines have a slope of 3/4
no, because the slopes of the lines are not equal.
no, because the slopes of the lines are not opposite reciprocals of each other.
don't copy answers off of sites, otherwise i'd report you
Both lines are parallel because: A. both lines have a slope of 4/3.
What is the Slope of a Line?The slope of a line = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
The slope of parallel lines are the same, while the slope of perpendicular lines are negative reciprocals.
Slope of AB = 4 units/3 units = 4/3
Slope of CD = 4 units/3 units = 4/3
Both lines have the same slope, therefore, they are parallel to each other.
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Which tables could be used to verify that the functions they represent are inverses of each other? Select two
options.
X
-120
27
-110
2
y
-100 -95 -90
27 227627
х
- 120
-110
27
y
2
100
27
-95
227
-90
627
х -120
y 627
-110
227
-100
27
-95
2
-90
27
х
y
627 227 27
-120 -110-100
2
-95
27
-90
627
227
y -90-110
27
-100
2 27
- 110 -120
Mark this and return
Save and Exit
Next
Submit
Based on the tables given and the functions represented, the two functions that are inverses of each other are Tables 3 and 4.
Which functions are inverses of each other?When two functions are said to be inverses of each other, it means that the value of x is one is the corresponding value of y in the other function.
For instance, when the point is (5, 16) in one function, the other function's point would be (16,5).
The functions that are inverses are therefore Tables 3 and 4 as shown attached.
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Which of the statements are true about the function f given by f(x) = 100-e? Select all that apply.
a The values of increase when x increases.
b The value off when x = 5 is less than 1.
d
e The value of is never 0.
E
The value of f when x=-1 is a little less than 40.
The y-intercept of the graph off is at (0, 100).
From the above function, it is clear that the value of f is never 0. Hence the statement that is true is (Option E), See explanation of same below.
What is the explanation for the above function?Note that the function is related to Euler's number which is depicted as:
e ≈ 2.7182. The function is given as:
f(x) = 100 * [tex]e^{-x}[/tex]
Assuming x = -2, we'd have:
100 * 2.7182[tex]^{-2}[/tex]
= 271.82[tex]^{-2}[/tex]
= 0.00001353354
Hence, even when x tends < 0 the function f(x) thus, is never 0. See the attached graph for confirmation.
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what are the key features of the graph of a trigonometric function? How do you find them from a graph or an equation?
Answer:
The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.
They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).
what is the measure of angle f
Answer:
What is the context, at least give a figure
1. Using the above
scatterplot, does there
seem to be a positive
correlation, a negative
or no
correlation,
correlation between
the number of
customers and sales?
Answer:
yes there is a correlation
Step-by-step explanation:
here's how I found this by looking up all key words.
A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−10)2+95. Which of the following statements is true?
The airplane reaches its maximum height of 10 feet in 95 seconds.
The airplane reaches its maximum height of 95 feet in 10 seconds.
The airplane reaches its minimum height of 95 feet in 10 seconds.
The airplane reaches its minimum height of 10 feet in 95 seconds.
Considering the given quadratic function, the correct statement is given by:
The airplane reaches its maximum height of 95 feet in 10 seconds.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient. If a > 0, the vertex is a minimum point, and if a < 0 it is a maximum point.
In this problem, the function is:
h(t) = -(t - 10)² + 95.
Hence the vertex is (10, 95), and since a < 0, the correct statement is given by:
The airplane reaches its maximum height of 95 feet in 10 seconds.
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Simplify using BODMAS rule :
60÷6[{32÷4(7×2-15+5)}+3]
Step-by-step explanation:
the right answer is 1.714
I have a bag with 6 marbles numbered from 1 to 6. mathew has a bag with 12 marbles numbered from 1 to 12. matthew chooses one marble from his bag and i choose two from mine. in how many ways can we choose the marbles (where the order of my choices does matter) such that the sum of the numbers on my marbles equals the number on his?
Answer:
It would be 30.
Step-by-step explanation:
If we make a list of all the sums that we can get, we have:
1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6
These 15 sums can be chosen in two ways, since order matters, and we could do 2+1 instead of 1+2.
That gets us to 15x2 which is 30.
The number of ways that we can choose the marbles such that the sum of the numbers on my marbles equals the number on his would be 30.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
I have a bag with 6 marbles numbered from 1 to 6.
Mathew has a bag with 12 marbles numbered from 1 to 12.
1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6
These 15 sums can be chosen in two ways,
Since order matters, and we could do 2+1 instead of 1+2.
15 x 2 which is 30.
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Help please it is confusing
Answer:
(c) Yes, +4 more
Step-by-step explanation:
The problem statement is telling you the available quantity in pounds. The answer choices are expressing the difference in terms of packets. A conversion of units of measure is needed.
__
availablePatel has 8 pounds of seed, and he puts it into 1/2-pound packets. Each pound will fill two (2) half-pound packets, so he has enough for ...
(8 lb) × (2 packets/lb) = 16 packets
neededPatel has 12 people planting seed, so needs 12 of the 16 packets in order to give each team member one packet.
He has enough seed for this need, and enough for 16 -12 = 4 more packets than he needs.
Aisha has a piece of string that she cuts into smaller pieces. This line plot shows the length of each piece. Juan has a piece of string that is 12 as long as Aisha's seventh-longest piece. (Note: The problem states the seventh-longest piece, not the seventh-longest length.)
How long is Juan's piece of string?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
2 5/8 inches
Step-by-step explanation:
There are 2 pieces 5 3/4 inches long.
There is 1 piece 5 1/2 inches long.
There are 4 pieces 5 1/4 inches long.
The seventh longest piece is one of the pieces measuring 5 1/4 inches.
Juan's piece is 1/2 as long as 5 1/4 inches.
1/2 × 5 1/4 inches = 1/2 × 21/4 = 21/8 inches = (16/8 + 5/8) = 2 5/8 inches
Consider two circular swimming pools. Pool A has a radius of 18 feet, and Pool B has a diameter of 11.16 meters. Complete the description for which pool has a greater circumference. Round to the nearest hundredth for each circumference. 1 foot ≈ 0.305 meters
The diameter of Pool A is
17.24
meters. So, the diameter of Pool
A
is greater, and the circumference is
greater
by
meters.
Answer:
The circumference of Pool B is greater than the circumference of Pool A by about 0.56 meters
Step-by-step explanation:
Identify the diameter of Pool A.
d = 2r
d = 2(18) Substitute 18 for r.
d = 36 ft
Convert from feet to meters. Use the ratio of 1 foot to 0.305 meters.
36 × 0.305 = 10.98
The diameter of Pool A is about 10.98 meters.
Use the formula to find the circumference of Pool A.
C = πd
C = π(10.98) Substitute 10.98 for d.
C ≈ 3.14(10.98) Substitute 3.14 for π.
C ≈ 34.48 Multiply. Round to the nearest hundredth.
The circumference of Pool A is about 34.48 meters.
Identify the diameter of Pool B.
d = 11.16 m
The diameter of Pool B is 11.16 meters.
Use the formula to find the circumference of Pool B.
C = πd
C = π(11.16) Substitute 11.16 for d.
C ≈ 3.14(11.16) Substitute 3.14 for π.
C ≈ 35.04 Multiply. Round to the nearest hundredth.
The circumference of Pool B is about 35.04 meters.
The circumference of Pool B is greater than the circumference of Pool A.
Find how much greater the circumference of Pool B is compared to the circumference of Pool A.
35.04 − 34.48 = 0.56
The circumference of Pool B is greater than the circumference of Pool A by about 0.56 meters.
Which of the following graphs shows the solution for the inequality
y-4> 2(x+2)?
Answer:
Answer:
Graph C shows the solution for the inequality
Step-by-step explanation:
y - 4 > 2(x + 2)
y > 2x + 4 + 4
y > 2x + 8
Let y = 2x + 8, Then
X-intercept (0, 8)
Y-intercept (-4, 0)
Since the inequality sign is > we use broken line.
Put, (0, 0)
y > 2x + 8
0 > 0+ 8
0 > 8 Which is false
so, the answer will be above the broken line
Hence , Graph C shows inequality
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If Randy sells 8 times as many vacuum cleaners as Janice, and Janice sells 690 vacuum cleaners per year, on average, how many does Randy sell each month
Randy sells, in average, 460 vacuum cleaners per month.
How many vacuum cleaners does Randy sell each month?.
First, we know that Janice sells 690 units per year.
There are 12 months in a year, so the amount that she sells, in average, per month is:
J = 690/12 = 57.5
This means that Janice sells, in average, 57.5 units per month. And Randy sells 8 times as many, then we can solve the product:
R = 8*57.5 = 460
This means that Randy sells 460 units per month.
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What number is missing from this factor tree for the prime factorization of 425?
A. 2
B. 3
C. 5
D. 7
I need help what's the answer
Answer:
[tex]y = 2x - 5[/tex]
Step-by-step explanation:
slope-intercept form is [tex]y = mx + b[/tex] with [tex]m[/tex] being the slope of the line and [tex]b[/tex] being the y-intercept (where the line touches the y-axis)
First we can find [tex]m[/tex] using the formula for slope, [tex]\frac{rise}{run}[/tex] (or [tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]), which is the change in y over the change in x.
We can use any points on the line, but I am going to use [tex](4, 3)[/tex] and [tex](3, 1)[/tex] for this example. We can now find the slope.
[tex]\frac{3-1}{4-3} = \frac{2}{1}[/tex]
This means your slope is 2, which means [tex]m[/tex] is 2.
Finding the y-intercept is easy. This line crosses the y-axis at -5, and so [tex]b[/tex] is -5.
Now we can plug in the values into our original equation to get the equation of the line.
[tex]y = 2x - 5[/tex]
That is the answer
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55 POINTS!!!!!! WILL GIVE BRAINLIEST!!!!!!! PLS HELP ASAP!!!!!
Danielle is trying to solve the equation [tex]8^x=\frac{1}{64}[/tex]. Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answer:
x=-2
Step-by-step explanation:
Given equation:
8^x= 1/64
Ensure both sides of the equation are in power format by changing 1/64
1/64 = 64^-1
8^x = 64^-1
2^3(x) = 2^6(-1)
The bases will cancel out each other
3(x) = 6(-1)
3x = -6
x = -6/3
x = -2
Check
8^x = 1/64
x = -2
8^-2
= 1/8²
= 1/8*8
= 1/64
Can someone help pls
Answer:
B.) No, because it fails the vertical line test.
Step-by-step explanation:
You can determine whether or not graphs represent functions by performing the vertical line test. This test states that to be a function, there must only be one output for every input. In other words, there must be only one "y" value per "x" value. As you can see, for some "x" values there is more than one "y" value.
The easiest way to perform this test is by placing your finger at the top of the graph and moving it downwards. If you cross the line twice, then it must not be a function.
What is the area of the trapezoid shown? The figure is not drawn to scale.
284.31 in.²
303.75 in.²
568.62 in.²
607.5 in.2
Answer:
284.3
Step-by-step explanation:
Trapezoid Formula:
A=a+b/2*h
plug in the numbers
I forgot how do do these anyone remember please
Answer:
x ≤ 1/2
Step-by-step explanation:
Domain: input values (x-values)
We cannot take a square root of a negative number, therefore
3 - 6x ≥ 0
Solving the inequality:
⇒ 3 - 6x ≥ 0
⇒ 3 ≥ 6x
⇒ 1/2 ≥ x
⇒ x ≤ 1/2
Therefore, the domain is x ≤ 1/2
Translate the shape A four squares right and two squares down.
please don't delete this question iltae668.
What are the coordinates of the vertices of the image?
What are the coordinates of the image of vertex G after
a reflection across the line y = x?
O (-4,-5)
O (4, 5)
O (-5,4)
O (5, 4)
Answer:
(- 5, 4 )
Step-by-step explanation:
under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
G (4, - 5 ) → G' (- 5, 4 )
The coordinates of the image of vertex G are (-5, 4)
What is line of reflection?When reflecting a figure in a line or in a point, the image is congruent to the pre image. A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
here, we have,
Let us revise some cases of reflection
If the point (x, y) reflected across the x-axis , then its image is (x, -y)
If the point (x, y) reflected across the y-axis , then its image is (-x, y)
If the point (x, y) reflected across the line y = x , then its image is (y, x)
If the point (x, y) reflected across the line y = -x , then its image is (-y, -x)
From the given figure
∵ The line of the reflection is y = x
→ That means we will switch the coordinates of the point to find its image
∵ The coordinates of vertex G are (4, -5)
∴ The x-coordinate = 4 and the y-coordinate = -5
→ Switch the two coordinates
∴ The coordinates of its image G' are (-5, 4)
∴ The coordinates of the image of vertex G are (-5, 4)
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need help fast given lim x→c f(x) = "-4" and lim x→c g(f) =1/5 what is lim x→c [g(f)/f(x)]
Work Shown:
[tex]\displaystyle \lim_{x \to c}f(x) = -4\\\\\\\lim_{x \to c}g(x) = 1/5\\\\\\L = \lim_{x \to c}\frac{g(x)}{f(x)}\\\\\\L = \frac{\displaystyle \lim_{x \to c}(g(x))}{\displaystyle \lim_{x \to c}(f(x))}\\\\\\L = \frac{1/5}{-4}\\\\\\L = (1/5)*(-1/4)\\\\\\L = -1/20\\\\[/tex]
Put simply, we divide the two given values g(x) = 1/5 over f(x) = -4 to end up with -1/20
Ariel has a salary of $100,000 in the year 2003 and got a raise of 3.32 % every year. How much money in total will Ariel earn up through the year 2007, to the nearest dollar?
You have a 3-gallon and a 5-gallon jug that you can fill from a fountain of water. The problem is to fill one of the jugs with exactly 4 gallons of water. How do you do it?
Answer:
See below
Step-by-step explanation:
Fill the 5 and pour into the 3 ....this will leave 2 gal in the 5 bucket
empty the 3 bucket and put that 2 gallon in to it.....
then fill the 5 bucket again......pour 1 gallon into the 3 gallon bucket to fill it....then there will be 4 gallons left in the 5 bucket
Find the midpoint of A and B where A has coordinates (2, 3)
and B has coordinates (8, 9).
Step-by-step explanation:
Solution,Given,Coordinates of A and B are (2,3) and(8,9) respectively. Let A(2,3)= (x1,y1) and B(8,9)=(x2,y2)Midpoint of AB(m)=?Now,using midpoint formulam= {(x1+x2)/2 ,(y1+y2)/2}or m= {(2+8)/2,(3+9)/2}.°. m=(5,6)Answer:Mxy= [(Xa+Xb/2);(Ya+Yb/2)]
=(2+8/2);(3+9/2)
Midpoint= (5, 6)
Step-by-step explanation:
Find a possible formula for the trigonometric function represented by the given table of values. (enter your answer in the form y = a cos(bx − c) d or y = a sin(bx − c) d. )
A function assigns the values. The function will be 8cos(2x-π)+4.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the maximum value is 12, while the minimum value is -4, therefore,
A = (Max-Min)/2 = 12-(-4)/2 = 8
D = (Max+Min)/2 = (12-4)/2 = 4
Period=π, but since x =-4 at 0 or π, therefore,
(2π/B) = π
B = 2π/π = 2
C/B = π/2, {∴At π/2 maximum}
C=π
Hence, the function will be 8cos(2x-π)+4.
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Find the 14 term of the following geometric sequence.
10, 20, 40, 80,
Answer:
81920
Step-by-step explanation:
Finding the common ratio (r) :
20/102Finding the 14th term :
a₁₄ = ar¹⁴⁻¹a₁₄ = ar¹³a₁₄ = (10)(2)¹³a₁₄ = (10)(8192)a₁₄ = 81920Answer:
the 14th term in the sequence would be 81920.
Step-by-step explanation:
because you are multiplying by 2 each time to find the next multiply 80 by 2 giving you 160 again giving you 320 again giving you 640 than 1280 , 2560 ,5120 ,10240 ,20480 ,40960 ,finally the 14th number in the sequence multiplying 40960 by 2 would give you your answer of 81920.