The range of the function f(x) = sin(x) given in the task content is; Negative 1 less-than-or-equal-to y less-than-or-equal-to 1; -1<= y <=1.
What is the Range of the function?The range of a function is simply the set of its possible output values. For instance, for the function f(x)=x⁴ on the domain of all real numbers , the range is the non-negative real numbers, which can be written using interval notation.
On this note, the range of the function as given is -1<= y <=1.
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Answer: B, the set of all real numbers Negative 1 less-than-or-equal-to y less-than-or-equal-to 1
Step-by-step explanation: edge
2x - 3 > 15 or 3 + 7x < 17
Answer:
2x-3>15 and 3-7x>17 =
3-7x>17
-7x>14
x<-2
Step-by-step explanation:
Sorry this is not a proper equation. I think you meant this equation.
2x-3>15 and 3-7x>17
for this equation the answer is
3-7x>17
-7x>14
x<-2
Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
Answer:
Step-by-step explanation:
y4−
(y2−9)(y2+9)
9
Distribute:
=y4+
−1
9
y4+9
Combine Like Terms:
=y4+
−1
9
y4+9
=(y4+
−1
9
y4)+(9)
=
8
9
y4+9
Answer:
=
8
9
y4+9
The polynomial expression is divisible by 9
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
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 polynomial be represented as A
Now , A = y⁴ - (y² - 9)(y² + 9)
To prove that the expression y⁴ - (y² - 9)(y² + 9) is divisible by 9 for any value of y, we can use algebraic manipulation and factorization.
First, we can simplify the expression inside the parentheses:
y² - 9 = (y - 3)(y + 3)
y² + 9 = (y + 3i)(y - 3i)
where i is the imaginary unit, i.e., i² = -1.
Substituting these expressions back into the original equation, we get:
y⁴ - (y² - 9)(y² + 9) = y⁴ - (y - 3)(y + 3)(y + 3i)(y - 3i)
Now, we can factor out (y − 3)(y + 3) from the second term:
y⁴ - (y² - 9)(y^2 + 9) = y⁴ - (y² - 9)(y² + 9) + 9(y - 3)(y + 3)
= y⁴ - (y² - 3^2)(y² + 3²)
= (y²)² - (3²)²
= (y² + 3²)(y² - 3²)
= (y² + 9)(y² - 9)
= (y + 3i)(y - 3i)(y + 3)(y - 3)
Now, we can see that the expression is equal to the product of four factors: (y + 3i), (y - 3i), (y + 3), and (y - 3). Note that either (y + 3i) and (y - 3i) or (y + 3) and (y - 3) must have the same residue modulo 3, since there are only three residues modulo 3 (0, 1, and 2) and four factors. In either case, the product of the two factors that have the same residue modulo 3 is divisible by 3, and therefore the entire expression is divisible by 3.
Moreover, since (y + 3) and (y - 3) are both odd or both even, the product of (y + 3) and (y - 3) is divisible by 8, which implies that the entire expression is also divisible by 8.
Hence , the expression y⁴ - (y² - 9)(y² + 9) is divisible by both 3 and 8 for any value of y, and therefore it is also divisible by their least common multiple, which is 9
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What is the measure of angle x
Answer:
x =83
Step-by-step explanation:
supplementary angles add to 180 degrees
x+y = 180
We know y is 97
x+97= 180
Subtract 97 from each side
x+97-97= 180-97
x =83
Answer:
It is 83
Step-by-step explanation:
Supplementary is 180 degrees
180-97=83
Angela is using a number cube for a game with faces labeled 1, 2, 3, 4, 5, and 6. Is the number cube fair? Explain why or why not.
Answer: Yes
Step-by-step explanation: It is equal because each side has a chance of it rolling on either 1,2,3,4,5, and 6.
Enter the value of the 8 in the following number. 438.13
Answer:
8
Step-by-step explanation:
It is in the one's place, so it is just 8x1, which is 8
Find the volume of this figure
Answer:
74
Step-by-step explanation:
you find the volume of each one by doing length * width * height and once you find the volume of all of them which is 36, 2, 36 you add them all together and you get 74
Answer:
74 ft
Step-by-step explanation:
Volume = length x width x height
For the 1st square - 3 x 3 x 4
For the rectangle in the middle - 1 x 1 x 2
For the last big square - 3 x 3 x 4
___________________________________
3 x 3 x 4 = 36
3 x 3 x 4 = 36
1 x 1 x 2 = 2
___________________________________
36 + 36 + 2 = 74
___________________________________
The volume of this figure is 74 ft
Please mark me as brainliest!!!
My phone rang midway between 10:53 A.M. one day and 1:05 P.M. the next day. It rang at
a) 11:58 P.M.
b) 11:59 P.M.
c) 12:59 A.M.
d) 1:59 A.M.
Step-by-step explanation:
So lets count the time between 10:53 and 1:05
7 Mins to 11
2 Hours to one
5mins to 1:05
Total 2 hours 12 mins divided by 2 to find the middle
1 hour 6 mins. We add 1 hr 6 mins to 10:53.
10:53 + 6mins equals 11:59
11:59 + 1hour = 12:59
Answer c
Can someone help me and show how to write the perimeter equation for x to this polygon.50 points Find x for full 70 points
Answer:
10x + 8 = 21
x = 1.3
Step-by-step explanation:
a)
In pentagon ABCDE,
AB = DE = 2x + 3 and BC = CD = x + 1
Perimeter of pentagon ABCDE = 21
4x + 2(2x + 3) + 2(x + 1) = 21
4x + 4x + 6 + 2x + 2 = 21
[tex] \purple {\boxed {\bold{10x + 8 = 21}}} [/tex]
b)
10x = 21 - 8
10x = 13
[tex]x = \frac{13}{10} \\ x = 1.3 \: cm [/tex]
Are the graphs of the lines in the pair parallel ? Explain.
Y=2/3x-17
3-x - y = -6
A.)Yes, since the slopes are the same and the y-intercepts are different.
B.)No, since the slopes are different.
C.)No, since the y-intercepts are different.
D.)Yes, since the slopes are the same and the y-intercepts are the same.
So the right answer is of option D
Look at the attached picture
Hope it will help you...
Good luck on your assignment
Is this SAS or Not SAS
Answer:
yes it is sas
Step-by-step explanation:
because one side is shared, they both have right angles and the other side is a given.
Answer:
SAS
Step-by-step explanation:
The sides are all equivalent so it is indeed a SAS triangle.
Percentages equal to 100% and how?
Answer:
2 or more percents add up to 100% or one percent is 100%
Step-by-step explanation:
I need help with this please!
Answer:
The equation of a circle using the center [tex](2,0)[/tex] and the radius [tex]7[/tex]
[tex](x-2)^2+(y-0)^2= 49[/tex]
Step-by-step explanation:
-Directions:
To determine the following circle on a graph, you need the to look for a point that lands exactly on the center of the circle and to find the radius, you need look for a point that lands exactly on the outline of the circle and start counting from the center, to the point. Then, use both the center and the radius for the equation of a circle. After putting the center and radius on the equation of a circle, simplify the radius by the exponent [tex]2[/tex], because according to the equation of a circle, the radius is [tex]r^2[/tex].
-The equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]
-Finding the center and the radius for the equation of a circle:
Center: [tex](2,0)[/tex] Radius: [tex]7[/tex]
[tex](x-2)^2+(y-0)^2= 49[/tex]
The grades on a geometry midterm at Springer are roughly symmetric with u = 73 and 0 = 3.0.
Umaima scored 72 on the exam.
Find the z-score for Umaima's exam grade. Round to two decimal places.
Answer:
z = - 0.33
Step-by-step explanation:
Given that:
Mean (μ) = 73, standard deviation (σ) = 3.0
Z score is a measure in statistics to determine the number of standard deviation a value is above or below the mean of what is measured. If the value is above the mean it is positive but if it is below the mean it is negative. It is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
To calculate z-score for Umaima's exam grade, we need to calculate the z score of 72
For x = 72, the z score is:
[tex]z=\frac{x-\mu}{\sigma}=\frac{72-73}{3} =-0.33[/tex]
z = - 0.33
Answer:
−0.33
Step-by-step explanation:
just did it oh khan
Which values are solutions to the inequality below
Check all that apply
What is the solution to the inequality |X-4|<3?
-7
1
x < -7 or x < -1
x> 1 or x<7
mutlak değerden + veya- çıkar.
|X-4|<3
-3 <x-4 <3
-3+4 <x <3+4
1 <x <7
The solution to the inequality |x-4| < 3 is x> 1 or x<7
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality,
|x-4| < 3.
Simplifying,
-3 < x - 4 < 3
Adding 4 to all sides,
1 < x < 7
Therefore, the solution is 1 < x < 7.
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Which value in this data set is an outlier?
4,5, 1, 7,4,5,8,9,6,5,4,9,7
O A 1
OB. 2
3
OD
9
Answer:
1 is the out lier
Step-by-step explanation:
if you put them in order: 1, 4, 4, 4, 5, 5, 5, 6, 7, 7, 8, 9, 9
They are in order exept for the one.
The marked price of a water cooler is $ 4500. The shopkeeper offers an off-season discount of 18% on it. Find its selling price.
Answer:
$3690
Step-by-step explanation:
Let's first find what percent of the original price it is being sold for.
100%-18%=82%
The water cooler is being sold for 82% of its original price.
Let's now find 82% of 4500.
0.82*4500=3690
The selling price is $3690
Answer:
3690
Step-by-step explanation:
the original price is 4500
for decreasing or discount we use this formula x discount upo 100 multiply by the original price. so for this question if we apply the formula it will be
18upon 100 x4500. the answer comes as 810. noww we subtract the original price from the discounted price. so 4500-810=3690. comes as ur selling price
The playing field for a particular sport is a rectangle whose length is 4 feet more than twice the width. The perimeter of the playing field is 200 feet. Find the dimensions of the playing field.
Answer:
The length and width of the field are 68ft and 32ft respectively
Step-by-step explanation:
Given:
Rectangular Playing Field
Perimeter. P = 200 ft
Required
The dimension of the field (Length and Width)
Let L and W represent the length and the width of the field.
From the question, L is 4 more than twice of W.
This means
L = 4 + 2W
Provided that the playing field is rectangular in shape;
We need to make use of the formula of perimeter of a rectangle.
P = 2(L + W)
Substitute 200 for P
200 = 2(L + W)
Divide through by 2
[tex]\frac{200}{2} = \frac{2(L + W)}{2}[/tex]
100 = L + W
Recall that L = 4 + 2W
Substitute 4 + 2W for L
100 = L + W becomes
100 = 4 + 2W + W
100 = 4 + 3W
Subtract 4 form both sides
100 - 4 = 4 + 3W - 4
96 = 3W
Divide both sided by 3
[tex]\frac{96}{3} = \frac{3W}{3}[/tex]
32 = W
W = 32
Recall that L = 4 + 2W
Substitute 32 for W
L = 4 + 2(32)
L = 4 + 64
L = 68
Hence the length and width of the field are 68ft anf 32ft respectively
A rectangle is 36 inches x 48 inches.
Pin.
What is its perimeter?
What is its area?
Answer:
Area is: 1,728 inches
Perimeter is: 168 inches
Step-by-step explanation:
Area= Length times width
Perimeter= length plus length plus width plus width.
Answer:
1.728 is the perimeter. the area is 84.
Step-by-step explanation:
all you do multiply for perimeter and add for area.
The equations 4 x minus 5 y = 5, 3 x + 10 y = 20, 4 x minus 5 y = negative 5, and 3 x + 10 y = negative 20 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, 1) and (2.5, 3). Orange line goes through (0, negative 1) and (2.5, 1). Blue line goes through (0, 2) and (3.5, 1). Pink line goes through (0, negative 2) and (3.5, negative 3). Which system of equations has a solution of approximately (–2.7, –1.2)? 4 x minus 5 y = negative 5 and 3 x + 10 y = negative 20 4 x minus 5 y = 5 and 3 x + 10 y = 20 4 x minus 5 y = 5 and 3 x + 10 y = negative 20 4 x minus 5 y = negative 5 and 3 x + 10 y = 20
Answer:
First one:
4 x minus 5 y = negative 5 and 3 x + 10 y = negative 20
Step-by-step explanation:
4 x - 5 y = -5 (1)
3 x + 10 y = -20 (2)
Multiply (1) by 2 and add to (×)
8x - 10y = -10
3x + 10y = -20
11x = -30
x = -30/11 = -2.727272
x = -2.7
4(-30/11) - 5y = -5
5y = -65/11
y = -13/11 = -1.18181818
y = -1.2
Answer:
4 x - 5 y = - 5 and 3 x + 10 y = - 20
Step-by-step explanation:
4 x - 5 y = -5 (1)
3 x + 10 y = -20 (2)
Multiply (1) by 2 and add to (×)
8x - 10y = -10
3x + 10y = -20
11x = -30
x = -30/11 = -2.727272
x = -2.7
4(-30/11) - 5y = -5
5y = -65/11
y = -13/11 = -1.18181818
y = -1.2
hope this helps..
Alina has been collecting video games for a year. The table below shows how many games she has received over
the year.
Amount of video games
4
Birthday
Holidays
School trades
8
6
At the end of the year, she went to a store and sold half of her video games.
Which numerical expression shows the amount of video games Alina has left after selling half?
Choose 1 answer:
(4+8) + (6 + 2)
2 : (4 +8+6)
© (4+8+6) : 2
The numerical expression shows the amount of video games Alina has left after selling half will be (4 + 8 + 6):2. Then the expression C is correct.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Alina has been collecting video games for a year. The table below shows how many games she has received over the year.
Amount of video games
Birthday 4
Holidays 8
School trades 6
Then the total number of the video games will be
⇒ 4 + 8 + 6
At the end of the year, she went to a store and sold half of her video games.
⇒ (4 + 8 + 6) / 2
⇒ (4 + 8 + 6) : 2
Then the expression C is correct.
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The measure of an exterior angle of a triangle is equal to which of the following measures?
A. The measure of its complementary angle
B. The measure of its adjacent angle
C. The sum of the measures of the interior angles
D. The sum of the measures of its remote interior angles
Answer:
C. The sum of the measures of the interior angles
Step-by-step explanation:
An exterior ∠ is equal to the addition of the two Δ angles not right next to it.The 2 exterior angles at each vertex are = in measure because they are vertical angles.
• The exterior angles (taken one at a vertex) always total 360º
After the dimensions of an equilateral triangle are increased by a scale factor of 2.5, the perimeter is 45 units. What were the side lengths of the original triangle?
Answer:
Original side of triangle = 6 units
Step-by-step explanation:
Given:
Perimeter = 45 units
Scale factor = 2.5 (Increase)
Find:
Original side of triangle = ?
Computation:
Original Perimeter = Perimeter / Scale factor
Original Perimeter = 45 units / 2.5
Original Perimeter = 18 units
Perimeter of an equilateral triangle = 3 (Side)
18 units = 3 (Side)
Side = 6 units
Original side of triangle = 6 units
f(x) = 5x^2 - x + 8
g(x) = 9x - 1
Answer:
Step-by-step explanation:
But there is not a question?
A circle with circumference 6 has an arc with a
340º central angle.
Answer:
17.80236
Step-by-step explanation:
There are two groups of people, three in each, for painting a wall. The numbers in the next two sentences express the time (in hours) spent on painting. In group A, Alex 2.5, Adam 3.6, and Antimo 4.7. In group Z, Zairo 2.2, Zeno 3.2, and Zubro 4.9. Estimate the total time for group A and for group Z when all three workers in each group work together. Which group can paint the wall faster and why do you think so?
(your answer is two numbers
(two estimates) in one sentence where you will explain your reasoning)
Answer:
1. The total time taken for group A to paint the wall together is 1.12 hours
2. The total time taken for group Z to paint the wall together is 1.03 hours
3. group Z can paint the wall faster
Step-by-step explanation:
The time spent on painting are;
Group A
Alex = 2.5 hours
Adam = 3.6 hours
Antimo = 4.7 hours
1. We have for group A
Alex's paint rate = 1 wall in 2.5 hours = 1/2.5 wall/hour
Adam's paint rate = 1 wall in 3.6 hours = 1/3.6 wall/hour
Antimo's paint rate = 1 wall in 4.7 hours = 1/4.7 wall/hour
When the three workers work together, we have;
1/2.5 wall/hour + 1/3.6 wall/hour + 1/4.7 wall/hour = 3767/4230 wall/hour
Therefore, the time for the three workers of group A to paint one wall is given as follows;
[tex]Time \ to \ paint \, one \, wall = \frac{1 \, wall}{\frac{3767}{4230} wall/hour} = 1\tfrac{463}{3767} hours[/tex]
The total time taken for group A to paint the wall together = 1.12 hours
2. The data for group Z is as follows;
Zairo = 2.2 hours
Zeno = 3.2 hours
Zubro = 4.9 hours
We have for group Z
Zairo's paint rate = 1 wall in 2.2 hours = 1/2.2 wall/hour
Zeno's paint rate = 1 wall in 3.2 hours = 1/3.2 wall/hour
Zubro's paint rate = 1 wall in 4.9 hours = 1/4.9 wall/hour
When the three workers work together, we have;
1/2.2 wall/hour + 1/3.2 wall/hour + 1/4.9 wall/hour = 8375/8624 wall/hour
Therefore, the time for the three workers of group Z to paint one wall is given as follows;
[tex]Time \ to \ paint \, one \, wall = \frac{1 \, wall}{\frac{8375}{8624} wall/hour} = 1\tfrac{249}{8375} hours[/tex]
The total time taken for group Z to paint the wall together = 1.03 hours
3. Since the total time for group A to paint the wall which is 1.2 hours is more than the total time for group Z to paint the wall which is 1.03 hours, group Z can paint the wall faster.
find the missing angle in the triangle
Answer:
45
Step-by-step explanation:
Because this is an isosceles triangle, two of the angles must be equal. Since the third angle is 90 degrees, the other two must be 90/2=45 degrees. Hope this helps!
I will give you brainliest if you answer correctly!!
Answer:
The answer is B.
Step-by-step explanation:
how many solutions does : 3y = -6x + 9
y = -6x + 9
Answer:
Exactly 1 solution
Step-by-step explanation:
First we must disrupte3y+27=12y+13
Next we switch one number to the other side27=9y+13
Now we must switch the other number14=9y
Now we must solve by dividing 14 by 9y=1.555
This is one solution, so we now have our answer.
The equation has only one solution. Then the correct option is A.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equations are given below.
3y = -6x + 9
y = -2x + 3 ...1
y = -6x + 9 ...2
From equations 1 and 2, then we have
-2x + 3 = -6x + 9
4x = 6
x = 6/4
x = 1.5
Then the value of the variable 'y' is calculated as,
y = -2x + 3
y = -2(1.5) + 3
y = - 3 + 3
y = 0
The solution of the equation y = -2x + 3 and y = -6x + 9 will be (1.5, 0). Then the equation has only one solution. Then the correct option is A.
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What is the area of the base of a cylinder with a volume of 174π in.3 and a height of 12 inches?
Answer:
The area of the base is 14.5π in²
Step-by-step explanation:
The volume of a cylinder is given by
Volume =base\:area \times height
Or
V=Bh
It was given that the volume of the cylinder is 174π in³.
The height was given as 12 inches.
We substitute to get,
174π=12B
Divide both sides by 12 to get:
B=14.5π in²
Hence the area of the base is 14.5π in²
Hope this helpsBrainliest plzand have a wonderful dayAnswer:
area of base = 14.5π in²
Step-by-step explanation:
the area of the base of a cylinder with a volume of 174π in^3 and a height of 12 inches is found by applying the formula for the volume of a cylinder:
V = πr²h
Here the area of the base of a cylinder with a volume of 174π in³ and a height of 12 inches, and so:
V = πr²(12 in) = 174 π in³
Dividing both sides by 12 in isolates πr², which is the area of the base:
174π in³
area of base = πr² = --------------- = 14.5π in²
12 in
