Given the expression:
[tex]\sqrt[]{-81}[/tex]As we know, there is no square root for the negative numbers
But, using the complex numbers:
[tex]i=\sqrt[]{-1}[/tex]So, the given expression can be written as:
[tex]\sqrt[]{-81}=\sqrt[]{-1}\cdot\sqrt[]{81}=i\cdot9=9i[/tex]So, the answer will be option A) 9i
9. The exchange rate of a certain foreign currency with the Indian rupee is Rs 62.50.How much of the foreign currency can be had for Rs3125 ?
Answer
Rs. 3125 is equivalent to 50 units of the foreign currency.
Step-by-step Explanation
The exchange rate of the foreign currency in Indian Rupee is Rs. 62.50
This means that
1 unit of that foreign currency = Rs. 62.50
Or better written as
Rs. 62.50 = 1 unit of the foreign currency
So, we are then told to find how much Rs. 3125 is in the foreign currency
Let Rs. 3125 be equal to x units of the foreign currency
Rs. 62.50 = 1 unit of the foreign currency
Rs. 3125 = x units of the foreign currency
A simple mathematics relation obtained by cross multiplying will give us the value of x
After cross multiplying
62.50 × x = 3125 × 1
62.50x = 3125
Divide both sides by 62.50
(62.50x/62.50) = (3125/62.50)
x = 50
Therefore, Rs. 3125 is equivalent to 50 units of the foreign currency.
Hope this Helps!!!
Name a postulate or theorem that can be used with the given information to prove that the lines are parallel<3 ~ <7
Postulates and Theorems of Parallel Lines
First, we need to know what type of angles are <3 and <7. Following the definition:
If two lines are crossed by another line, the angles in matching corners are called Corresponding Angles.
Angles 3 and 7 are corresponding angles and they are told to be congruent.
Now we apply the postulate that reads:
The Converse of the Corresponding Angles Postulate. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
The postulate that can be used to prove that the lines are parallel is The Converse of the Corresponding Angles Postulate
How many degrees was ABCDE rotated? (submit your answer as a number)
If a figure has a vertex, (x, y) and it is rotated 180 degrees counterclockwise, the corresponding vertex of the new image would have a coordinate of (- x, - y)
Looking at the given figure, we would compare the corresponding coordinates of a given vertex. Looking at vertex A,
For the original figure, the coordinate is (1, 3)
For the ratated figure, the coordinate of A' is (- 1, - 3)
This corresponds to what was we stated earlier
Thus, it was rotated 180 degrees in the counterclockwise direction
In Exercises 25–26, the domain of each piecewise function is (-⬁,⬁). a. Graph each function. b. Use the graph to determine the function’s range.
We have to graph this piecewise function.
It will be two horizontal lines that change when x = -1: to the left it will be y = 5, as x ≤ 1, and to the right, it will be y = -3.
We can see it graphed as:
b) The range is the set of values that f(x) takes for the domain for which it is defined.
We can see that f(x) only takes two values: y = -3 and y = 5, so the set {-3,5} is the range of f(x).
Answer:
a) Graph
b) Range = {-3, 5}
Graph the functions on the same coordinate plane.f(x) = −5g(x) = x^2 + 2x − 8What are the solutions to the equation f(x) = g(x)? Select each correct answer.−5−3−113
ANSWER
[tex]\begin{equation*} -3,1 \end{equation*}[/tex]EXPLANATION
The graphical solution to the given equation is obtained at the points where the two graphs of the two functions intersect each other on the coordinate plane.
To graph f(x), we simply draw a straight horizontal line at the point y = -5.
To graph g(x), we have to find coordinate points by substituting values of x into the function and obtaining values for g(x).
Let us find the value of g(x) when x = -3, -1, 1:
[tex]\begin{gathered} x=-3: \\ g(-3)=(-3)^2+2(-3)-8=9-6-8 \\ g(-3)=-5 \\ x=-1: \\ g(-1)=(-1)^2+2(-1)-8=1-2-8 \\ g(-1)=-9 \\ x=1: \\ g(1)=(1)^2+2(1)-8=1+2-8 \\ g(1)=-5 \end{gathered}[/tex]Now, we have three points to plot the graph with: (-3, -5), (-1, -9), (1, -5)
Let us now plot the graphs of the functions:
Therefore, the solutions to the equation f(x) = g(x) are:
[tex]\begin{gathered} x=-3,x=1 \\ \Rightarrow-3,1 \end{gathered}[/tex]If a red and a blue fair six sided die are rolled what is the probability the result is 8 or divisible by 3?
SOLUTION:
Step 1:
In this question, we are given that;
If a red and a blue fair six-sided die are rolled.
What is the probability the result is 8 or divisible by 3?
Step 2:
The table for the two dice rolled together is as shown below:
Green 1 2 3 4 5 6
Red
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Step 3:
The probability that the result is 8 =
[tex]\begin{gathered} =\text{ }\frac{\nu mber\text{ of 8}}{\text{Total number }} \\ =\text{ }\frac{5}{36} \end{gathered}[/tex]Next,
The probability that the result is divisible by 3
=
[tex]\frac{12}{36}[/tex]Finally, the probability that the result is 8 or divisible by 3, we have that:
[tex]\frac{5}{36}+\frac{12}{36}\text{ =}\frac{17}{36}[/tex]
A triangle has two sides of length 13 and 17. What is the largest possible whole numberlength for the third side?
Given two sides of a triangle, x, and z, such that
[tex]x\le z[/tex]then the third side y must satisfy the following condition
[tex]z-xIn our case,x =13, and z = 17
Then, the third side y
lies in
17-13 < x < 17 +13
4 < x < 30
Hence the largest possible whole number of the third side is 29
A ball is thrown in the air. It's height, h (in meters).is given by h = -4.91 +306 + 6 where is thetime (in seconds). What is the height of the ballafter 3 seconds?
The given equation-
[tex]-4.9t^2+30t+6[/tex]After three seconds, we evaluate for t = 3.
[tex]-4.9(3)^2+30(3)+6=-4.9(9)+90+6=-44.1+96=51.9[/tex]Therefore, the height after 3 seconds is 51.9 meters.I need help pls 1. Is this graph sine or cosine 2. What’s the amplitude of graph 3. What’s the equation of the midline 4. Whats the period of the function Whats the equation of the function Whats the domain and range?
As per given by the question,
There are given that a graph.
Now,
1. The given graph is cosine graph.
2. The aplitute of the given graph is,
From the graph, it is lie between -2 to 2.
So,
The amplitude of the given graph is 2.
Now,
3. The equation of the midline is,
[tex]y=-2[/tex]Now,
4.The period of the fumction is,
[tex]P=\frac{2\pi}{3}[/tex]Now,
The equation of the function.
First the general form of cosine graph function is,
[tex]y=A\cos (bx+c)+d[/tex]Then,
[tex]y=2\cos (3x+c)+d[/tex]Now,
[tex]y=2\cos (3x-1)+3[/tex]Where, D is vertical shift.
Hence, the equation of the function is,
[tex]y=2\cos (3x-1)+3[/tex]Find the value of x assume the triangles are the same
1) In this problem, we need to find the constant of proportionality assuming these triangles are similar. So let's divide each corresponding leg:
[tex]\frac{22}{18}=\frac{33}{27}\Rightarrow\:k=\frac{11}{9}[/tex]2) So, based on that constant of proportionality (k) we can find the missing leg.
[tex]\begin{gathered} x\div\frac{11}{9}=36 \\ \\ x\cdot\frac{9}{11}=36 \\ \\ 11\times\frac{9}{11}x=36\times11 \\ \\ 9x=396 \\ \\ \frac{9x}{9}=\frac{396}{9} \\ \\ x=44 \end{gathered}[/tex]Note that since the triangle on the top is larger than the one on the bottom, we can tell that x must be larger than 36.
Look at this graph: 100 90 80 60 50 20 10 10 20 30 50 60 70 80 90 100 What is the slope? Simplify your answer and write it as a proper fraction, improper fraction or integer. Submit Not feeling yet These con heo
To find the slope of the line we have to use this equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Now we have to replace two coordiantes in the line, so I was able to see the coordinates: (0,40) and (20,50), sothe equation become:
[tex]m=\frac{50-40}{20-0}[/tex]and we simplify so:
[tex]m=\frac{10}{20}=\frac{1}{2}[/tex]So the slope is 1/2
If the m< P is 65 degrees, then what is the measure of Arc XY
Answer:
[tex]\text{ArcXY}=115\text{ degrees}[/tex]Step by step explanation:
We can solve this situation by the theorem of the angle formed outside of a circle by intersection:
*For two tangents:
[tex]mThen, if m
[tex]\begin{gathered} 65=\frac{1}{2}((360-mXY)-mXY) \\ 65=\frac{1}{2}(360-\text{mXY-mXY)} \\ 65=\frac{1}{2}(360-2\text{mXY)} \\ 65=180-\text{mXY} \\ \text{mXY}=180-65 \\ \text{mXY}=115 \end{gathered}[/tex]
PLEASE HELP
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, the team observes that the angle of elevation to the top of the mountain is 25o. From a point 1,000 feet closer to the mountain along the plain, the team finds that the angle of elevation is 29o. How tall (in feet) is the mountain? Round to two decimal places.
The height of the mountain is 2936.39 feet.
Given,
In the question:
The angle of elevation to the top of the mountain is 25°.
To find the height of the mountain, we can draw triangles as in the image attached.
Now, According to the question:
Let's call the height of the mountain 'h', and the distance from the first point (25degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(29) = h/x
tan(25) = h/(x+1000)
tan(25) is equal to 0.4663, and tan(29) is equal to 0.5543, so:
h/x = 0.5543 -> x = h/0.5543
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.5543 + 1000) = 0.4663
h = 0.4663 * (h/0.5543 + 1000)
h = 0.8412h + 466.3
0.1588h = 466.3
h = 466.3 / 0.1588 = 2936.39 feet
Hence, the height of the mountain is 2936.39 feet.
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Give the equation of the line parallel to a line through (-3, 4) and (-5, -6) that passes through the origin. y = 5x y = 5x + 1 y=-1/5x + 1 y = -1/5x y
To solve for the equation of the line parallel :
[tex]\begin{gathered} (-3,4)\Longrightarrow(x_1,y_1) \\ (-5,-6)\Longrightarrow(x_2,\text{y}_2) \end{gathered}[/tex]For parallel line equation:
Slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept
First let's find the slope of the line.
To find the slope using two points, divide the difference of the y-coordinates by the difference of the x-coordinates.
[tex]\begin{gathered} \text{slope =}\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-6-4}{-5--3} \\ \text{slope=}\frac{-10}{-5+3}=\frac{-10}{-2} \\ \text{slope =5} \end{gathered}[/tex]Slope= 5
[tex]\begin{gathered} y=mx+c \\ y=5x+c \\ \text{where c = y-intercept} \end{gathered}[/tex]The y-intercept is (0, b). The equation passes through the origin, so the y-intercept is 0.
[tex]\begin{gathered} y=5x+0 \\ y=5x \end{gathered}[/tex]Hence the
Lindsay gets paid $15 per hour at her job. If we let s be her salary and h be the number of hours she has worked, write an equation that represents the direct variation.
A linear function or a direct variation function is represented by:
[tex]y=kx[/tex]where k is the constant rate of chante, in this case $15 per hour.
s=y= salary of Lindsay
h=x= hours she has worked
Then, the equation that represents the situation would be:
[tex]s=15h[/tex]What is the low end value, high end value, and does it have an outlier
Solution;
Given the results:
From the above data:
A) The low-end value is
[tex]0[/tex]B) The high end value is
[tex]95[/tex]C) Does this data set have outlier?
[tex]Yes[/tex]D) Outlier:
[tex]95[/tex]I need help solving
This problem
Weight required to destroy a bridge cable (in ponds) The type of variable is Nominal Categorical
A frequently used category variable is gender. Categorical variables can either be ordinal or numeric.
The closing price (in dollars) of the stock is a quantitative variable, and since the price involves an absolute zero, the scale of measurement is a ratio scale
Pounds is what type of variable?
Weight is a prime example of a ratio variable (e.g., in pounds). With certainty, we may state that 20 pounds weigh twice as much as 10 pounds. Ratio variables also have an important zero-point (e.g., exactly 0 pounds means the object has no weight)..
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fine one value of x for which f(x) = 4 and find f(0)look at the graph below
To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]Please help and no I cannot show a picture of it. 5+5×0+5
Answer:
Solving the expression gives;
[tex]5+5\times0+5=10[/tex]Explanation:
Given the expression;
[tex]5+5\times0+5[/tex]Applying the rule of BODMAS or PEMDAS;
multiplication comes first;
[tex]\begin{gathered} 5+5\times0+5 \\ 5+0+5 \end{gathered}[/tex]Then we can do the addition;
[tex]\begin{gathered} 5+0+5 \\ =5+5 \\ =10 \end{gathered}[/tex]Therefore, solving the expression gives;
[tex]5+5\times0+5=10[/tex]find the area of each. use your calculator's value of pi. round your answer to the nearest tenth.
We are asked to find the area of the given circle.
Recall that the area of a circle is given by
[tex]A=\pi r^2[/tex]Where π is a constant and r is the radius of the circle.
From the figure, we see that the diameter is 22 km
Recall that the radius is half of the diameter.
So, the radius of the circle is
[tex]r=\frac{D}{2}=\frac{22}{2}=11\: km[/tex]So, the area of the circle is
[tex]A=\pi r^2=\pi(11)^2=\pi\cdot121=380.1\: km^2[/tex]Therefore, the area of the circle is 380.1 square km (rounded to the nearest tenth)
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 2". Let B be the event "the outcome is greater than 4". Find P(A or B). Outcome Probability 1 0.15 2 0.31 3 0.35 4 0.08 5 0.11
The general rule of P(A or B) is given by the formula
[tex]undefined[/tex]Maria used a hundred chart to find a sum. She started at 57 then she moved down 3 rows and back 2 spaces which number did she land on
She landed on the number 25 on the hundred chart.
What is an 100 chart?
It consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows.
We are given that she was on 57th number
Then she moved down 3 rows
Each row contains 10 elements Hence we subtract 30 for 3 rows
57-30=27
Then also she took 2 steps back
Hence we again subtract 2 from 27
We get 27-2=25
Hence she is at 25th number
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60 cars to 24 cars The percent of change is
We can calculate the percent of change by means of the following formula:
[tex]change=\frac{x2-x1}{x1}\times100[/tex]Where x2 is the new value and x1 is the original value.
In this case, we go from 60 to 24, then the original value (x1) was 60 and the new value (x2) is 24, by replacing these values into the above equation, we get:
[tex]change=\frac{24-60}{60}\times100=-60[/tex]Then, the percent of change equals -60%
Pls help! No ive asked 5 tutors and they cant do it!
The sampling distribution can be approximated to follow the normal distribution if the sample size is large, and the values of 'np' and 'n(1-p)' are much greater than 10.
Consider option A,
[tex]\begin{gathered} np=30\times0.3=9 \\ n(1-p)=30\times(1-0.3)=21 \end{gathered}[/tex]Consider option B,
[tex]\begin{gathered} np=22\times0.4=8.8 \\ n(1-p)=22\times(1-0.4)=13.2 \end{gathered}[/tex]Consider option C,
[tex]\begin{gathered} np=30\times0.8=24 \\ n(1-p)=30\times(1-0.8)=6 \end{gathered}[/tex]Consider option D,
[tex]\begin{gathered} np=22\times0.5=11 \\ n(1-p)=22\times(1-0.5)=11 \end{gathered}[/tex]It is observed that only the values in option D, give that 'np' and 'n(1-p)' are greater than 10. Therefore, option D will be the correct choice.
See attached for the problem
The areas and volumes are given as follows:
a) Area of the four sides to be painted: 2448 m².
b) Area to be covered with shingles: 1140 m².
c) Volume of concrete needed to pour a floor 16 cm deep: 174.72 m³.
d) Total surface area: 5878.4 m².
Area -> Four sides paintedThe sides painted are divided as follows:
Two rectangles of dimensions 26 m and 18 m.Two rectangles of dimensions 42 m and 18 m.Hence the total area to be painted is found as follows:
Total area = 2 x 26 x 18 + 2 x 42 x 18 = 2448 m².
(Area rectangle = base x height)
Area to be covered with shinglesThis part of the problem seems incomplete, however the answer is correct.
Volume of concreteThe volume is given by:
Volume = base area x height.
Hence:
The base area is a rectangle of dimensions 26 m and 42 m.The height is of 16 cm = 0.16 m.Hence the volume is given by:
V = 26 x 42 x 0.16 = 174.72 m³.
Surface areaThe base is a rectangular prism of dimensions 26 m, 42 m and 18m, hence:
Surface area base = 2 x (26 x 42 + 26 x 18 + 42 x 18) = 4632 m².
The top is composed by:
Two rectangles of dimensions 13.6 m and 42 m.Two triangles of base 26 m and height 4 m.Hence:
Surface area top = 2 x 13.6 x 42 + 2 x 0.5 x 26 x 4 = 1246.4 m².
Then the total surface area is:
Total surface area = 4632 + 1246.4 = 5878.4 m².
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For the rotation 707°, find the coterminal angle from 0° ≤ 0 < 360°, thequadrant and the reference angle
Explanation
We are required to determine the coterminal, quadrant and reference angle of 707°.
This can be achieved as:
Therefore, the reference angle can be gotten as:
[tex]720\degree-707\degree=13\degree[/tex]Hence, the reference angle is 13°.
The angle lies in the fourth quadrant.
The cotermi
Need to find the domain, range, x-intercept, y-intercept, and rate of change from the graph
Explanation
Step 1
Domain:The domain of a function is the complete set of possible values of the independent variable, by the graph is it a continuous line, so the domain is
[tex](-\infty,\infty),[/tex]Step 2
Range:The range is the set of all second elements of ordered pairs (y-coordinates), by the graph is it a continuous line, so the range is
[tex](-\infty,\infty),[/tex]Step 3
x-intercept
it is when y= 0 , by the graph :
[tex](-2,0)[/tex]Step 4
y-intercept
it is when x= 0 m by the graph:
[tex](0,4)[/tex]Step 5
rate of change
Let
P1(-2,0) P2(0,4)
[tex]\begin{gathered} rate\text{ of change=}\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{0-(-2)}=\frac{4}{2}=2 \\ \end{gathered}[/tex]rate of change:2
Mrs. Smith stores water in different size bottles. she has 4 containers that are 2 1/2 quarts each and 3 containers that are 425 cups each. how many fluid ounces of water does she have?
Answer:
The total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]Explanation:
Given that she has 4 containers that are 2 1/2 quarts each
[tex]\begin{gathered} V_1=4\times2\frac{1}{2}\text{ quarts} \\ V_1=10\text{ quarts} \end{gathered}[/tex]Recall that to convert quarts to ounce;
[tex]1\text{ quart }=32\text{ ounces}[/tex][tex]\begin{gathered} V_1=10\text{ quarts }=10\times32\text{ ounces} \\ V_1=320\text{ ounces} \end{gathered}[/tex]Also, she has 3 containers that are 4.25 cups each;
[tex]\begin{gathered} V_2=3\times4.25\text{ cups} \\ V_2=12.75\text{ cups} \end{gathered}[/tex]To convert cups to ounces;
[tex]1\text{ cup}=8\text{ ounces}[/tex]So;
[tex]\begin{gathered} V_2=12.75\text{ cups }=12.75\times8\text{ ounces} \\ V_2=102\text{ ounces} \end{gathered}[/tex]The total volume of fluid ounces of water she have is;
[tex]V=V_1+V_2[/tex]substituting the values;
[tex]\begin{gathered} V=320+102\text{ ounces} \\ V=422\text{ ounces} \end{gathered}[/tex]Therefore, the total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]Mr. Baker wants to divide his class into smaller, equal-sized groups of students.
However, he finds that his class cannot be divided evenly into any size group except for individual groups of 1.
Complete the statements below about the number of students in Mr. Baker's class.
The completion of the statements about the number of students in Mr. Baker's class is as follows:
The number of students in his class must be a prime number.The quotient from the division of the students into equal-sized groups is not even because there must be a remainder.What is a prime number?A prime number is a number divisible by itself and 1 only.
When a prime number is divided by another number except by itself and 1, there is always a remainder in the quotient.
Some examples of the prime numbers in Mr. Baker's class include 19, 23, 29, 31, or 37 students.
Thus, these numbers of students cannot be divided by another number without a remainder because they are prime numbers.
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Question Completion:1. The number of students in his class must be a --- number.
2. The quotient from the division of the students into equal-sized groups is .... because there must be a .....
May I ask a question?if I have a 10 girls in a class and the total number of students in the class are 30, what's the percentage of the total amount of girls?
Given:
The number of girls =10 and the total number of students =30.
The percentage of the total amount of girls is
[tex]=\frac{The\text{ number of girls}}{\text{The total number of students}}\times100[/tex][tex]=\frac{10}{30}\times100[/tex][tex]=33.33[/tex]Hence the percentage of the total amount of girls is 33.33 %.