The real square roots of -121 are ±11i, where 'i' represents the imaginary unit.
Explanation:When dealing with square roots of negative numbers, it's important to recognize that the square root of a negative number is an imaginary number. In this case, the square root of -121 is found by taking the square root of the positive value of 121 and then multiplying the result by 'i'. The square root of 121 is 11, so the square root of -121 becomes ±11i.
In the context of real numbers, square roots of negative values do not exist. However, in the realm of complex numbers, the introduction of the imaginary unit 'i' allows for the representation of square roots of negative numbers. The number 'i' is defined as the square root of -1. When squared, 'i' multiplied by itself yields -1.
Hence, the square root of -121, which is a negative number, results in ±11i, representing two imaginary numbers with opposite signs. These imaginary square roots are crucial in various fields, including mathematics, physics, and engineering, where complex numbers play a significant role in modeling and solving problems involving quantities with both real and imaginary components.
XY and BD are parallel lines.
X is a point on AB and C is a point on BD.
XB = XC.
a) Complete this sentence.
Angle XBC = 55⁰ because
b) Work out angle BXC.
Give a reason for each angle you work out.
Answer:
Hey i got the top one its AXY and XBC ar corresponding angles
Step-by-step explanation:
help it helps you ,i will look and try to do the bottom one aswell, kan you mark me the brainlist pls.
Final answer:
Angle XBC equals 55° because of the Alternate Interior Angles Theorem applied to the parallel lines XY and BD. Angle BXC in triangle XBC is worked out to be 70° due to the Angle Sum Property of a triangle, considering triangle XBC is isosceles with XB equal to XC.
Explanation:
Angle Measurements in Parallel Lines and Triangles
When considering XY and BD as parallel lines, and points X on AB and C on BD such that XB = XC, we can analyze the angles formed using the properties of parallel lines and triangles.
a) Angle XBC = 55° because of the Alternate Interior Angles Theorem, which states that when two parallel lines are crossed by a transversal, the alternate interior angles are congruent. Since XY and BD are parallel, and AB is a transversal, angle XBC is congruent to the alternate interior angle on the opposite side, which must also measure 55°.
b) To work out angle BXC, consider triangle XBC which is isosceles given that XB = XC. Since angle XBC is 55° and triangle XBC has two equal sides (XB and XC), the base angles (XBC and XCB) are equal. So angle XCB is also 55°. The sum of all angles in a triangle is 180°, so angle BXC = 180° - (55° + 55°) which equals 70°.
The reason that angle BXC is 70° is due to the Angle Sum Property of a triangle, which is the sum of angles in a triangle is always 180°.
How do I find X? I have to show work as well.
Answer:
d
Step-by-step explanation:
Answer:
YOU FIND X BY CAN U MARK ME AS BRAINLIEST????
Step-by-step explanation:
MULTIP[LYING ALL OF THE SIDES AND NUMBERS THEN THAT IS YOUR ANSWER
Factor Completely: 3x squared+ 15x - 72
Answer:
actor Completely: 3x squared+ 15x - 72
3x²+15x-72
(x+5) (5x-24)
Step-by-step explanation:
solve for x in the diagram in the pic
Answer:
x=34
Step-by-step explanation:
The angle measure of a straight line is 180 degrees.
So if you add up all of the angles to make an equation, you get 2x + 112=180.
Then solve.
2x + 112=180
-112
2x=68
x=34
What is the test that you can do to tell if a graph represents a function?
A. the horizontal line test
B. the vertical line test
C. the expression test
D. the litmus test
Answer:
I think it's gonna be c
Step-by-step explanation:
C The expression test
find the area of the regular polygon
Answer:To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.
Step-by-step explanation:
hope this helps
plez mark as brainlyest
A square napkin is folded in half on the diagonal and placed on the diameter of a round plate
(see diagram below).
If the folded napkin spans the plate and the plate has an 18-inch diameter, what is the area of
the space on the plate that is NOT covered by the napkin? Leave your answer in terms of .
Answer:
The area of the space on the plate that is not covered by the napkin is[tex]81(\pi-1)\ in^2[/tex]
Step-by-step explanation:
step 1
Find the area of the plate
The area of a circle is given by the formula
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=18/2=9\ in[/tex] ---> the radius is half the diameter
substitute
[tex]A=\pi (9)^{2}\\A=81\pi\ in^2[/tex]
step 2
Find the area of the square napkin folded (is a half of the area of the square napkin)
we know that
The diagonal of the square is the same that the diameter of the plate
Applying Pythagorean theorem
[tex]D^2=2b^2[/tex]
where
b is the length side of the square
we have
[tex]D=18\ in[/tex]
substitute
[tex]18^2=2b^2[/tex]
solve for b^2
[tex]b^2=162\ in^2[/tex] -----> is the area of the square
Divide by 2
[tex]162/2=81\ in^2[/tex]
step 3
Find the area of the space on the plate that is NOT covered by the napkin
we know that
The area of the space on the plate that is NOT covered by the napkin, is equal to subtract the area of the square napkin folded (is a half of the area of the square napkin) from the area of the plate
so
[tex]A=(81\pi-81)\ in^2[/tex]
simplify
[tex]A=81(\pi-1)\ in^2[/tex]
The angle θ=π3 is in standard position and has a terminal side that coincides with the graph of a proportional relationship represented by y=kx.
a. Find the constant of proportionality, k.
b. Write an ordered pair that lies on the graph of y=kx.
Part a
theta = pi/3
sin(pi/3) = sqrt(3)/2
cos(pi/3) = 1/3
tan(angle) = opposite/adjacent = rise/run = slope
tan(pi/3) = sin(pi/3)/cos(pi/3) = (sqrt(3)/2)/(1/2) = sqrt(3)
The value of k is k = sqrt(3)This is also the slope the line y = kx because it is in the form y = mx+b with m = sqrt(3) and b = 0.
===============================================
Part b
Pick any value you want for x, and plug it in to find the paired value of y
if x = 0, then y = 0 because
y = sqrt(3)*x = sqrt(3)*0 = 0
So (0,0) is one ordered pair on the line---------
If x = 1, then y = sqrt(3), since,
y = sqrt(3)*x = sqrt(3)*1 = sqrt(3)
We can say ( 1, sqrt(3) ) is another ordered pair---------
If x = sqrt(3), then,
y = sqrt(3)*x = sqrt(3)*sqrt(3) = sqrt(3*3) = sqrt(9) = 3
Therefore, ( sqrt(3), 3 ) is another ordered pairThere are infinitely many ordered pairs on this line.Find the volume of a triangular pyramid with a base height of 5 inches, base length of 3 inches, and a height of 6 inches.
Final answer:
The volume of the triangular pyramid is calculated by finding the area of the triangular base and then using the volume formula for a pyramid, resulting in a volume of 15 cubic inches.
Explanation:
To find the volume of a triangular pyramid, we use the formula for the volume of a pyramid, which is V = (1/3) × base area × height. First, calculate the area of the triangular base using the formula for the area of a triangle, A = (base length × base height) / 2. In this case, the base length is 3 inches, and the base height is 5 inches.
Therefore, the area of the triangle is A = (3 in. × 5 in.) / 2 = 7.5 in.². Now, we can calculate the volume of the pyramid using the height of the pyramid, which is 6 inches.
The volume of the pyramid is V = (1/3) × 7.5 in.² × 6 in. When you calculate this, you get V = 15 in.³, which is the volume of the pyramid.
PLS HELP IM DOING THIS NOW and IDU, Students from Williams Middle School are also recycling aluminum cans. The data for the numbers of cans brought in each school day for a month were divided by quartiles and summarized in the box plot. Use the drop-down menus to choose the median, interquartile range, and range.
>Median:
>Interquartile range:
>Range:
Given:
Students from Williams Middle School are also recycling aluminum cans. The data for the numbers of cans brought in each school day for a month were divided by quartiles and summarized in the box plot.
We need to determine the Median, Interquartile range and Range.
Median:
The median is the middle value of the given set of data.
From the box plot, it is obvious that the median line is at 18.
Thus, Median = 18
Hence, the value of the median is 18.
Interquartile range:
The interquartile range is can be determined by finding the difference between the ends of the box in the box plot.
From the box plot, we have;
Interquartile range = 20 -16
Interquartile range = 4
Hence, the value of the interquartile range is 4.
Range:
The range can be determined by subtracting the highest and the lowest value in the given set of data.
From the box plot, the range can be determined by subtracting the ends of the line.
Thus, we have;
Range = 28 - 10
Range = 18
Hence, the value of the range is 18.
Answer:
Median: 18
Interquartile range: 4
Range: 18
Step-by-step explanation:
I just did this on edgen so this is the correct answer.
Line l is a straight line.
Which statements are true about the angles in the figure? Select two options
Answer:
The first and second are correct
Step-by-step explanation:
∠X and ∠Y and ∠W and ∠Z are linear angles and supplementary angles, and ∠Y and ∠Z are complementary angles. Then the correct options are A, B, and E.
What is an angle?Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
∠X and ∠Y are linear angles and supplementary angles.
∠W and ∠Z are linear angles and supplementary angles.
∠Y and ∠Z are complementary angles.
More about the angled link is given below.
https://brainly.com/question/15767203
Please help me answer this question
Answer:
C
Step-by-step explanation:
Your slope (m) is 1 and your y-intercept (b) is -9
y = mx + b
y = x - 9
f(x) also means y
Please make my answer the brainliest if its helpful
12y=24x
6x=3y+5
Which statement best describes the relationship between the lines?
Answer: i think is A they are parallel
Step-by-step explanation: is not perpendicular NOT-B
The relationship between the lines represented by the equations 12y = 24x and 6x = 3y + 5 is that they are parallel lines. This conclusion is drawn from the fact that they have the same slope (2) but different y-intercepts (0 for the first line and -5/3 for the second line).
Explanation:To determine the relationship between the lines represented by these equations, we must first put them in slope-intercept form (y = mx + b), where m represents the slope of the line, and b indicates the y-intercept.
For the first equation, 12y = 24x, we can divide both sides of the equation by 12 to get y = 2x.
For the second equation, 6x = 3y + 5, we re-arrange the equation by subtracting 5 from both sides and then dividing by 3. This gives us y = 2x - 5/3.
From the equations y = 2x and y = 2x - 5/3, we can see that the slopes of both lines are the same which is 2. This indicates that the lines are parallel to each other. However, since the y-intercepts are different (0 for the first line and -5/3 for the second line), we can conclude that they are different parallel lines, not the same line.
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are there whole numbers that are not rational numbers.
What is the mean for the data set?
{39, 43, 46, 86, 22, 39, 75}
Drag and drop the correct answer into the box.
mean ASAP
What is the perimeter, to the nearest hundredth of a unit, of the the
following polygon with vertices (-3, 2), (1, 2), (3,-1),(0,-3), (-4, -3)?
Answer:
Step-by-step explanation:
I WILL BE GIVING 15 points and 5 stars and thanks. Please answer quickly. A housewares company wants to add a new size of mug to its collection of available products. Its original mug design has a height of 120 millimeters and a diameter of 96 millimeters, and the new mug will have a height of 100 millimeters, as shown. If the company wants the new mug to be geometrically similar to the original mug, what should the diameter of the new mug be?
a = 81 mm
b = 80 mm
c = 76 mm
d = 72 mm
Answer:
b 80 mm i think because removed 20 mm
Answer:
c
Step-by-step explanation:
if your taking 20 mm from hight you have to take 20 from the diameter
Mr.O'Connor had $90 to spend at a football game. He spent 31/45 on his ticket. Then, he spent 3/7 of his remaining money at the concession stand. While walking back to his seat, he saw a new hat on sale for $18. Did Mr. O'Connor have enough money left to buy the hat?
I am not sure what to do.
Answer:
no
Step-by-step explanation:
he starts with 90 bucks to find what the fraction represents you can multiply it by 2 to get an equal denominator of 90 then subtract 90-62 that'll give you 28 then it says he spent 3/7 so you do the same thing get an equal denominator by multiplying by 4 and get 28 and as they say whatever you do to the denominator is done to the numerator so 3 times 4 is 12 then you do 28-12 and you gets 16 which isn't enough to buy the hat. :)
Ronnie's Rentals
charges $25 plus $15 per hour to rent a
chain saw. David rented a chain saw for
5 hours. Write an expression to show how
you could calculate the total amount
David paid.
Answer:
15x5+25=x
Step-by-step explanation:
15 times 5 plus 25 = total amount paid
For approximately what period of time does the Moon stay in the sky a week after the full-moon day?
A) 12 hours after sunset
B) 12 hours after midday
C) 12 hours after midnight
D) 12 hours during sunrise
Answer:
C 12 hours after midnight
Step-by-step explanation:
I just answered this question
4. Suppose Tyler sprayed around the house for ants. Which formula would be used to find the number of ants still alive after a certain time if the number of ants was changing exponentially?
A. exponential decay
B. exponential growth
C. compound interest
D. cannot be determined from given information
I’m giving as much points as I can please help I need this right now
Answer:
I think that the answer is A.
Step-by-step explanation:
Laney builds a tower with wooden cubes. The bottom cubes edges are 8 centimeters long. The middle cubes edges are 2 centimeters shorter than the bottom cube. The top cubes edges are 2 centimeters shorter than the middle cube. What is the total volume of the cubes in the tower?
Laney builds a tower with wooden cubes The bottom cubes edges are 8 cm long The middle cubes edges are 2 cm shorter than the bottom cube The top cubes edges are 2 cm shorter than the middle cube what is the total volume of the cubes in the tower
A is a quadrilateral with two sets of parallel sides and 4 right
angles
Answer:
If you are asking for the type of quadrilateral, then it could be a rectangle or a square.
Te assembly started at 3:02pm. It ended at
3:58pm. How long was the assembly?
Answer:
The assembly was 56 minutes long
Step-by-step explanation:
Answer: The assembly lasted 56 minutes.
Step-by-step explanation:
If you just pay attention to the minutes (2 and 58 respectively), you can subtract the original amount from the end amount.
58-2=56
Sooo..... can anybody help.....
Factor completely 3x^2+33x+90=?
Answer:
3(x+5) (x+6)
Step-by-step explanation:
The factored form of 3x² + 33x + 90 is: 3(x + 6)(x + 5)
To factor completely the quadratic expression 3x² + 33x + 90, we can look for two binomial factors that multiply together to give us the original expression.
First, we can check if the expression can be factored by using the common factor 3:
3x²+ 33x + 90
We can factor out 3 from each term:
3(x^2 + 11x + 30)
Now, we need to find two binomial factors that multiply to give us x² + 11x + 30.
The factors can be determined by factoring the quadratic expression further:
x² + 11x + 30 = (x + 6)(x + 5)
Therefore, the completely factored form of 3x² + 33x + 90 is:
3(x + 6)(x + 5)
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Jackie cut a piece of paper along its diagonal, as shown below, forming two triangles.
A rectangle is cut diagonally to form 2 equal triangles.
How do the height and base length of the two triangles compare to the height and base length of the original piece of paper?
The two dimensions are the same in the triangles as they were in the rectangle.
The two heights are the same in the triangles as they were in the rectangle, but the bases of the triangles are half the length of the base of the rectangle.
The two bases of the triangles have the same length as the base of the rectangle, but the triangles have heights equal to half the height of the rectangle.
The two dimensions of the triangles are each half what they were in the rectangle.
Answer:
B. The two dimensions are the same in the triangles as they were in the rectangle.
Step-by-step explanation:
Given
Initial Shape: Rectangle (Before cut)
Final Shape: Triangles (After cut)
Note that this can be explained properly with the use of attachments
See attachment 1 for Before Cut
Before Cut represent the full rectangle before Jackie cut the piece of paper.
Let H and B represent the height and base of the triangle
Given that the rectangle is cut diagonally, this means that the cutting starts and ends at the opposite edges of the rectangle
See attachment 2 for After Cut
After Cut represent the two triangles after cutting the rectangle
From the attachment, you'll observe that the dimension of the two triangles (Triangle 1 and Triangle 2) are the same as it is with the rectangle;
In other words, the two triangle have their heights as H and their bases as B.
Hence, it can concluded that the two dimensions are the same in the triangles as they were in the rectangle.
Answer:
c is the correct answer
Step-by-step explanation:
What is the length of each leg of the triangle below?
Answer: answer is f
Step-by-step explanation:
Answer:
F
Step-by-step explanation:
3.4.3
Someone pls help me with this question I’ll mark as brainliest
Answer:
A.
Step-by-step explanation:
The ball height goes from 3 to 7 in 2 seconds.
7-3=4
4/2 is 2.
Therefore A. is correct.
10−y=2.301
please find y
Answer:
y = 7.699
Step-by-step explanation:
10−y=2.301
subtract 10 from both sides
10-10−y=2.301-10
-y =-7.699
Multiply each side by -1
y = 7.699