Two angles are complementary. If one angle measures 32 degrees, what is the measure of the second angle?
If one angle measures 32 degrees, the measure of the second angle can be found by subtracting 32 from 90. Therefore, the second angle is 58 degrees.
Explanation:Complementary angles are two angles whose sum is 90 degrees. So, if one angle measures 32 degrees, we can find the measure of the second angle by subtracting 32 from 90:
Second angle = 90 - 32
Second angle = 58 degrees
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1. How many parts does each complex number have? What are they?
2. What kind of numbers are a and b in a complex number?
3. Give 4 examples of complex numbers. Identify the real numbers (a and b) (not parts) in your examples.
4. In a complex number in the form a + bi, what is the real coefficient of i?
5. Show and explain how you can write real numbers, such as 6, or -7.2 as complex numbers.
6. Give 2 examples of real numbers written in complex form.
7. Show and explain how you can write imaginary numbers, such as 23i or -0.24i as complex numbers.
8. Give two examples of imaginary numbers written in complex form.
9. What is the modulus of 5 - 3i ?
Will give more points once answered fully and correctly
14/40 in simplest form
A chief had 6 cups of berries and will use 2/3 cup of berries for each serving of fruit salad. How many servings can be made ?
The price of a stock had a change of –3 dollars.
Explain how you would use a number line to find the absolute value of –3
Hello! The answer to your question is: Draw out a horizontal line. Place 0 at the center. Then place evenly spaced tick marks on either side of 0. Label the right side of tick marks as 1, 2, 3, moving from 0 and going to the right
Label the left side of tick marks -1, -2, -3, starting at 0 and moving left
The location -3 on the number line is exactly 3 units away from 0. We start at 0 and move to -3 by moving 3 spots to the left; or we start at -3 and move 3 units to the right to get to 0.
Therefore, the absolute value of -3 is 3
Absolute value on a number line is the distance a number is from 0
The distance is never negative.
Hope this helped!
List the theorems for finding zeros of higher degree polynomial functions?
Rational Root Theorem
Final answer:
The theorems for finding zeros of higher degree polynomials include the Fundamental Theorem of Algebra, which guarantees n roots for an nth degree polynomial, the quadratic formula for second-order polynomials, and Euler's Theorem for Homogeneous Functions. These tools and theorems assist us in identifying possible roots and understanding the behavior of polynomial functions.
Explanation:
Theorems for Finding Zeros of Higher Degree Polynomial Functions
There are several important theorems relevant to finding zeros or solutions of higher degree polynomial functions. One key theorem is the Fundamental Theorem of Algebra, which states that every nth-degree polynomial has exactly n complex roots, which may include repeated roots. Additionally, polynomials are continuous and differentiable, so finding points where the derivative is zero leads to identifying potential maxima and minima.
The quadratic formula is used to find the zeros of second-order polynomials, revealing up to two roots, which may be real or complex numbers. Another relevant theorem is Euler's Theorem for Homogeneous Functions, which pertains to homogeneous functions of a certain degree and their properties. In the case of polynomials, it can be applied to determine certain types of symmetries and relationships amongst the coefficients.
Regarding polynomials of odd degrees, these always have at least one real root. Furthermore, since real-world numbers are approximations, tiny changes in the coefficients of a polynomial can lead to distinct roots. It's also worth noting that for any nth degree polynomial, differentiation yields an n-1 degree polynomial, which guides us in understanding the number of maxima or minima the function can possess. This is illustrated by the derivative of a third-order polynomial being a second-order polynomial, which can have at most two real roots.
if 3x - 14 equals 2x + 10 what is 3x - 14
In the equation 3x - 14 = 2x + 10, the solution for x is 24. Substituting x = 24 into the expression 3x - 14 gives a result of 58. Therefore, the value of 3x - 14 under these conditions is 58.
Explanation:The student's question introduces an equation where two expressions are set equal to each other: 3x - 14 and 2x + 10. To find the value of 3x - 14, we first need to solve this equation for x.
To do so, we subtract 2x from both sides to get x - 14 = 10. We then add 14 to both sides to get x = 24. Thus, the value for 'x' that makes the two expressions equal is 24. Substituting 'x' into 3x - 14 gives us 3*24 - 14, which calculates to be 58.
Therefore, the value of 3x - 14 when 3x - 14 equals 2x + 10 is 58.
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A gardener determines the cost of planting daffodil bulbs to be $2.40 per square foot. How much will it cost to plant daffodil bulbs in a rectanglular garden that is 12 feet longand 5 feet wide?
A)$40.80
B)$60
C)$144
D)$81.60
The required cost to plant daffodil bulbs in a rectangular garden is $144 .
Given that,
A gardener determines the cost of planting daffodil bulbs to be $2.40 per square foot.
To determine the cost to plant daffodil bulbs in a rectangular garden that is 12 feet long and 5 feet wide.
The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
Here,
The area of the rectangular garden = 12 * 5
= 60 ft²
cost of planting daffodil bulbs = 2.40 * 60
= $144
Thus, the required cost to plant daffodil bulbs in a rectangular garden is $144.
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Mr. Baker’s fifth grade class of buried a time capsule in the field behind the school they drew a map and mark the location of the capsule with an ax so that his class can dig it up in 10 years what could Mr. Baker’s class have done to make the capsule easier to find
Change this decimal to a fraction
The repeating decimal [tex]\(0.1 \overline{23}\)[/tex] is equivalent to the fraction [tex]\(\frac{611}{5000}\)[/tex].
To convert the repeating decimal [tex]\(0.1 \overline{23}\)[/tex] to a fraction, let's denote it as x:
[tex]\[ x = 0.1 \overline{23} \][/tex]
Now, we can manipulate the decimal to eliminate the repeating part. Multiply both sides of the equation by an appropriate power of 10 to shift the decimal:
[tex]\[ 100x = 12.323232\ldots \][/tex]
Now, subtract the original equation from the manipulated equation to eliminate the repeating part:
[tex]\[ 100x - x = 12.323232\ldots - 0.1 \overline{23} \][/tex]
Simplify:
[tex]\[ 99x = 12.22 \][/tex]
Now, solve for x:
[tex]\[ x = \frac{12.22}{99} \][/tex]
To simplify the fraction, find the greatest common divisor (GCD) of 12.22 and 99, which is 1. Divide both the numerator and denominator by the GCD:
[tex]\[ x = \frac{12.22}{99} = \frac{611}{5000} \][/tex]
So, [tex]\(0.1 \overline{23}\)[/tex] as a fraction is [tex]\(\frac{611}{5000}\)[/tex].
how do I find the area of this shape
A father is ten times as old as his daughter. In 5 years he will be just five times as old as she will be. How old are they now? HELP PLEASEEE
The given problem is an algebraic equation where the daughter's age is denoted as 'x' and the father's age as '10x'. An equation is formulated to solve for 'x' based on future ages. The solution to the problem is that the daughter is 5 years old, and the father is 50 years old.
Explanation:The problem asked is a classic example of algebra problem solving. We are told that a father is 'ten times as old as his daughter', and in five years, 'he will be just five times as old as she will be'. Let's denote the daughter's current age as 'x'. Therefore, the father's current age will be '10x'.
In five years, the daughter will be 'x+5' and the father will be '10x+5'. At this future moment, the father is 'five times as old as the daughter', so we can create the equation: 10x + 5 = 5(x + 5). Solving this equation leads to 'x=5'. So, the daughter is 5 years old and the father is 50 years old.
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Jean's bedroom is 14 feet by 13 feet. She has chosen a carpet which costs $30.90 per square yard. This includes installation.
Determine her cost to carpet her room. $
A bag has 10 marbles and 4 are black. Joseph picks 2 marbles without replacing the first. What is the probability that both are black?
To find the probability that both marbles drawn by Joseph are black, you need to consider the number of ways he can draw 2 black marbles out of the 4 black marbles in the bag, divided by the total number of ways he can draw 2 marbles from the 10 marbles in the bag without replacement. The probability is 2/15.
Explanation:To find the probability that both marbles drawn by Joseph are black, we need to consider the number of ways he can draw 2 black marbles out of the 4 black marbles in the bag, divided by the total number of ways he can draw 2 marbles from the 10 marbles in the bag without replacement.
Let's calculate:
Therefore, the probability that both marbles are black is 6/45, which simplifies to 2/15.
Alexis said the area of 1/3 of the trapezoid is greater than the area of 1/6 of the hexagon because 1/3 >1/6. does her statement make sense?
Alexis's comparison of fractions does not suffice to determine which shape's fractional area is greater without knowing the total areas of the trapezoid and hexagon. The areas of shapes are calculated differently and must be considered before applying fractional parts to compare.
Alexis's statement does not necessarily make sense because the comparison she is making is only between the fractions
1/3 and 1/6, not the actual areas of the shapes. The area of a fraction of a shape depends on the total area of that shape. Therefore, without knowing the specific areas of the trapezoid and hexagon, we cannot conclude that
1/3 of the trapezoid has a greater area than 1/6 of the hexagon simply because 1/3 is greater than 1/6. To correctly compare the areas, one would need to know the total area of both shapes before fractions are applied.
Furthermore, when discussing the properties of shapes and areas, it is important to remember that the area of a trapezoid is calculated differently from the area of a hexagon. The area of a trapezoid is the average of the two bases multiplied by the height, whereas the area of a regular hexagon can be found by dividing it into equilateral triangles and calculating the area of those. Thus, the total area of each shape before fractions are considered plays a crucial role in determining if Alexis's statement is true or false.
If the spinner is spun 100 times, how many times would you expect it to land in region E? Explain.
Finding theoretical probability throwing a dart in a 3x3 yellow square that is centered inside a 6x6 blue square
rachel uses grid paper to plan a mural to paint at her school. the design will be made of two connected rectangles. the larger rectangle will have an area between 35 square feet and 45 square feet. the smaller rectanglewill have an area between 10 square feet and 20 square feet. Draw and label a diagram to show what Rachel could plan. Explain how to find the total area.
Billy is flying his new radio-controlled helicopter around town. He is using a map in which each grid line is equivalent to 100 feet. Billy releases the helicopter from the library parking lot, at (2, 6) on the map. He gets it to cruising altitude and then starts measuring its flight. Billy flies the helicopter in a direct line to the town pool, at (6, 9) on the map. How far has the helicopter flown?
The helicopter has flown a distance of 500 feet as calculated using the Euclidean distance formula for two points on a grid.
Explanation:To find the distance the helicopter has flown, we need to calculate the Euclidean distance between the two points (2,6) and (6,9) on the grid map. We can use the formula: Distance = √[(x₂ - x₁)² + (y₂ - y₁)²], where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points. Substituting the given points into the formula, we have:
Distance = √[(6 - 2)² + (9 - 6)²] = √[(4)² + (3)²] = √[16 + 9] = √25 = 5 grid lines.
Given that each grid line is equivalent to 100 feet, the helicopter has traveled 5 grid lines * 100 feet/grid line = 500 feet.
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If 60 of the 200 students are girls, then what percent of the students are girls?
Which choice represents the best rational approximation for *square root symbol* 3? A) 14/9 B) 15/13 C) 17/10 D) 6/5
A rational number is a number which is in the form [tex]\frac{p}{q} ,q \neq 0[/tex]
Now, the value of the number [tex]\sqrt 3 = 1.73[/tex]
Now let us evaluate each given rational number in decimal form.
[tex]\frac{14}{9} = 1.6\\ \\ \frac{15}{13} = 1.2\\ \\ \frac{17}{10} = 1.7\\ \\ \frac{6}{5} = 1.2[/tex]
Therefore, among these numbers, the best approximation is option c i.e. 17/10.
C is the correct option.
Answer:
C) [tex]\frac{17}{10}[/tex]
Step-by-step explanation:
[tex]1,732050808 ≈ \sqrt{3} \\ \\ 1,73 ≈ \sqrt{3}[/tex]
Therefore answer choice C) would be the best approximate answer to this:
* [tex]1\frac{7}{10} = 1,7[/tex]
I am joyous to assist you anytime.
Help please Math Geometry
Nich has a collection of books. He has 115 fantasy and science fiction books. These books are 46% of his collection. How many books does he have in his collection
if triangle ABC is rotated 180 degrees about the origin, what are the coordinates of A?
Answer:
The coordinates of A is [tex](-x_1,-y_1)[/tex].
Step-by-step explanation:
We are given that a triangle ABC is rotated 180 degrees about the origin .
We have to find the coordinates of A.
Let vertices of triangle ABC [tex]A(x_1,y_1),B(x_2,y_2) ,C(x_3,y_3)[/tex]
When we rotate the about 180 degrees then the coordinates changes like as
[tex](x,y)\rightarrow (-x,-y)[/tex]
When we rotate triangle ABC about 180 degrees then its vertices Ais ([tex]x_1,y_1)[/tex] change into [tex](-x_1,-y_1)[/tex]
Hence, the coordinates of A is [tex](-x_1,-y_1)[/tex].
Final answer:
After rotating triangle ABC 180 degrees about the origin, the coordinates of point A, initially at the origin (0, 0), remain unchanged at (0, 0).
Explanation:
If triangle ABC is rotated 180 degrees about the origin, the coordinates of point A after the rotation can be determined by applying the rules of rotation in the Cartesian coordinate system. Since point A is at the origin, its initial coordinates are (0,0). A rotation of 180 degrees about the origin will essentially reflect a point over both the x-axis and y-axis, but the location of point A will remain unchanged because it is located at the center of rotation. Therefore, the rotated coordinates of point A will still be (0, 0).
What is the attribute being measured?
A. Psi
B. Stress
C. glass rods
D. number of rods
Answer:
B. Stress
Step-by-step explanation:
Did the usa prept test :)
The tires on your bicycle have a radius of 8 inches. How many rotations does each tire make when you travel 700 feet? Round your answer to the nearest whole number. Please help me
Help ASAP..........idk what to do
Segment KL is tangent to ⊙ J. If KL¯¯¯¯¯¯≅JK¯¯¯¯¯, what is m∠J? The image is of a circle with centre P and having a sector KJM. KL is tangent to the circle. Points J, M and L are joined to form a horizontal line and thus a triangle KJL is formed.
That’s what it looks like. Im not sure how to solve it either though.
verify the identity sec(theta)sin(theta)cot(theta) = 1
Please solve both and tell me how!