ANSWER
[tex]2 \sqrt{3} i[/tex]
EXPLANATION
We we're given that, the real part of the complex number is 2.
Let the imaginary part be y.
Then the complex number is
[tex]z = 2 + yi[/tex]
Also, we have that, the modulus is 4.
The modulus is given by the formula;
[tex] |z| = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
This implies that,
[tex] 4 = \sqrt{ {2}^{2} + {y}^{2} } [/tex]
We square both sides to obtain;
[tex] {4}^{2} = 4 + {y}^{2} [/tex]
[tex]16 - 4 = {y}^{2} [/tex]
[tex] {y}^{2} = 12[/tex]
[tex]y = \sqrt{12} = 2 \sqrt{3} [/tex]
Therefore the complex part is
[tex]2 \sqrt{3} i[/tex]
Answer:
3.4
Step-by-step explanation:
i just did it
In which quadrant does the terminal side of the angle 387° lie?
Quadrant I
O Quadrant II
Quadrant III
Quadrant IV
Answer:
Quadrant I
Step-by-step explanation:
To find in which quadrant an angle is, you have to locate it between 0 and 360.
Since your angle is larger than 360 degrees, we subtract 360 degrees from it.... to get 27 degrees.
27 degrees and 387 degrees lie on the same spot, since they are exactly one turn around from each other.
Now, angles between 0 degrees and 90 degrees are in quadrant I
angles between 90 and 180 degrees are in quadrant II
Angles between 180 and 270 degrees are in quadrant III
Angles between 270 and 360 degrees are in quadrant IV
So, an angle of 27 degrees would land in Quadrant I.... so is 27 + 360x, where x is any integer representing a number of turns.
The answer is:
The terminal side of the angle 387° lies at the Quadrant I.
Why?We know that there are four quadrants on the plane, those quadrants goes from 0° to 360°, however, since the quadrant is going only from 0° to 360°, if we want to know where an angle greater than 360° is located, we need to take only the excess, so:
We are asked to find where the angle 387° is located, we can write the angle by the following way:
[tex]387\°=360\°+27\°\\[/tex]
So, we have that there are 27° more than 360°, if we want to find where the 367° we only need to locate where the excess (27°) angle is located.
Also, we know that:
Quadrant I: 0° to 90°
Quadrant II: 90° to 180°
Quadrant III: 180° to 270°
Quadrant IV: 270° to 360°
We have that 27° is between 0° and 90°, so, it's located on the first quadrant.
Hence, we have that the angle 367° is located at the Quadrant I.
Have a nice day!
Solve 5x + 7 > 17.
{x | x < 2}
{x | x > 2}
{x | x < -2}
{x | x > -2}
Answer:
[tex]\large\boxed{\{x\ |\ x>2\}}[/tex]
Step-by-step explanation:
[tex]5x+7>17\qquad\text{subtract 7 from both sides}\\\\5x>10\qquad\text{divide both sides by 5}\\\\x>2[/tex]
For the function f(x) = x^2, what effect will multiplying f(x) by 1/4 have on the
graph?
Answer:
the graph will be vertically compressed i just answered apex
Step-by-step explanation:
Answer:
The graph will be compressed vertically.
Step-by-step explanation:
FLED is definitely a parallelogram
Answer:
Yes that is true
because the lines on the opposite side will never intersect
Answer:
The correct option is A. FLED is definitely a parallelogram .
Step-by-step explanation:
From the given figure it is clear that the angle F and angle E are same. Angle L and angle D are same.
[tex]\angle F=\angle E[/tex]
[tex]\angle L=\angle D[/tex]
According to the properties of parallelogram, a quadrilateral is called parallelogram if and only if there are two pairs of congruent opposite angles (but not equal to 90°, otherwise it will be a square or rectangle).
Since we have two pairs of congruent opposite angles which are not a right angle, therefore the statement "FLED is definitely a parallelogram" is true.
Hence, option A is correct.
What are 5 ways that graph can be misleading ?
There are many ways that graphs can be misleading. Depending on how you set up your graph, the same set of data can look very different. It's important to understand that there are some common mistakes to avoid when making graphs. In addition, advertisers have been known to intentionally make their graphs misleading to make their data match their point.
In the image provided, this is a good example of a misleading graph.
First, notice that we know that the first bar is 10 and the second bar is 50. However, there are no labels on the horizontal or vertical axis so we don't know what the bars represent.
In addition, notice that there is no title on this graph. Since there is no title on the graph, we don't know anything about the data.
Further, look at the scale on the vertical axis. Notice that it's an uneven scale. The uneven scale makes it appear that the first bar is closer to the second bar than it actually is.
We could correct this graph by adding labels to the x and y-axis, adding a title to the graph, and making the scale on the vertical axis even.
Another way graphs can be misleading is using the wrong type to represent data. For example, a scatter plot might be better than a regular graph in some cases.
Lastly, graphs can be misleading by adding a wide range of numbers to show and increase or decrease relatively small to how it actually is.
In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.
Answer:
Sub into equation
Step-by-step explanation:
Answer: 2.775%
Step-by-step explanation:
Given: Mean : [tex]\mu=3,500\ g[/tex]
Standard deviation: [tex]\sigma=500\ g[/tex]
The formula to calculate z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 2,500g
[tex]z=\dfrac{2500-3500}{500}=\dfrac{-1000}{500}=-2[/tex]
The p-value of z = P(z<-2)=0.02275
In percent, [tex]0.02775\times100=2.775\%[/tex]
The percent of babies born in the United States are classified as having a low birth weight (< 2,500 g) = 2.775%
To the nearest 7739.5
Answer:
nearest whole = 7740
nearest ten = 7740
nearest hundred = 7700
nearest thousand = 8000
How many quarts of pure antifreeze must be added to 5 quarts of a 20% antifreeze solution to obtain a 30% antifreeze solution?
Answer:
5/7 quart
Step-by-step explanation:
Amount = concentration × volume
Amounts added = final amount
100% × x + 20% × 5 = 30% × (x+5)
Solving for x:
1.00x + 0.2×5 = 0.3×(x+5)
x + 1 = 0.3x + 1.5
0.7x = 0.5
x = 5/7
x ≈ 0.7
You should add 5/7 quart of pure antifreeze, or about 0.7 quart.
About 0.71 quarts of pure antifreeze should be added to 5 quarts of a 20% antifreeze solution to obtain a 30% antifreeze solution.
Explanation:To find out how many quarts of pure antifreeze must be added to 5 quarts of a 20% antifreeze solution to get a 30% antifreeze solution, we can set up the following equation:
0.2 * 5 + x = 0.3 * (5 + x) where x represents the amount of pure antifreeze to be added.
Solving this equation, we get:
1 + x = 1.5 + 0.3x,
This simplifies to 0.7x = 0.5,
So x = 0.5 / 0.7,
Therefore, About 0.71 quarts of pure antifreeze should be added to get a 30% solution.
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85% expressed as a fraction in simplest form is
Hello There!
85% = 85/100
85/100 = 0.85
0.85/1 * 100/100
85/100
SIMPLIFIED IS 17/20
Percent are always out of 100 so...
[tex]\frac{85}{100}[/tex]
Simplifying:
[tex]\frac{85}{100}/\frac{5}{5}=\frac{17}{20}[/tex]
Hope this helped!
What is the measure of <4?
Answer:
90°
Step-by-step explanation:
Two lines intersect each other at a right angle, making them perpendicular. Thus, the resulting angles will all be 90°, making ∠4 = 90°.
Alternatively, we can use the supplementary angles equation.
Let's call the right angle marked in the picture ∠5.
∠4 + ∠5 = 180°, since the line is also a straight angle which measures 180°.
∠4 + 90° = 180°
∠4 = 90°
Either way, ∠4 = 90°
Hope this helps!
if A/B and C/D are rational expressions, then which of the following is true?
Answer:
Option D. [tex]\frac{A}{B}*\frac{C}{D}=\frac{A*C}{B*D}[/tex]
Step-by-step explanation:
we have
[tex]\frac{A}{B}[/tex] and [tex]\frac{C}{D}[/tex]
we know that
To multiply fractions multiply the numerators of the fractions to get the new numerator and multiply the denominators of the fractions to get the new denominator
To divide two fractions, multiply the first fraction by the reciprocal of the second fraction
[tex]\frac{\frac{A}{B}}{\frac{C}{D}}=\frac{A}{B}*\frac{D}{C}[/tex]
and
[tex]\frac{A}{B}*\frac{C}{D}=\frac{A*C}{B*D}[/tex]
Ten times the square of a non zero number is equal to ninety times the number. What is the number?
Answer:
x=9
Step-by-step explanation:
Your number is 9.
Set this up as 10(x^2) = 90x where x > 0 or x< 0.
Factor by 10 on both sides.
10x(x) = 10x(9)
x=9
Hope this helped you!
Find the sum of the first 100
terms of the arithmetic
sequence
a1=15 and a 100=307
Answer:
16100
Step-by-step explanation:
n = 100
a1 = 15
a100 = 307
The first thing you have to do is solve for d
a100 = a1 + (n - 1)*d
307 = 15 + (100 - 1)*d
307 = 15 + 99*d
307 - 15 = 99*d
292 = 99 d
d = 292 / 99
d = 2.94949494
That's a real odd result, but it is what you get.
Sum = (a + L)*n/2
sum = (15 + 307)*n/2
Sum = 322 * 100 / 2
Sum = 16100 It looks like I didn't have to solve for d. The person who made this up sure didn't
\tan \left(18\right)=\frac{x}{20}
Answer:
x ≈ 6.5
Step-by-step explanation:
We have the epresion [tex]tan(18)=\frac{x}{20}[/tex] and we want to find the value of [tex]x[/tex].
Let's do it step-by-step
Step 1. Multiply both sides of the equation by 20
[tex]tan(18)=\frac{x}{20}[/tex]
[tex]20tan(18)=(\frac{x}{20} )(20)[/tex]
[tex]20tan(18)=x[/tex]
Step 2. use the reflexive property of equality: if [tex]a=b[/tex] then [tex]b=a[/tex]
[tex]20tan(18)=x[/tex]
[tex]x=20tan(18)[/tex]
Step 3. Using a calculator we get that [tex]tan(18)=0.325[/tex]. Replacing that value we get
[tex]x=20(0.325)[/tex]
x ≈ 6.5
We can conclude that the value of x is approximately 6.5
60 points
Please help answer, and If possible explain the questions. Thank you!
2. Which expression is not a polynomial?
A. X - 1
B. 4 + P
C. 5X^2 - √X
D. 8x - z^3
3. What is the degree of the polynomial?
3pq^4 - 2p^2q + q3
A.1
B.2
C.4
D.5
4. How many terms does the polynomial have?
p^3-4pq^2+q^2-3q
A.1
B.2
C.3
D.4
5. Which polynomial is written in standard form for the polynomial below?
-7x^2 - x^3 + x^5 +2
A. x^5+X^3+X^5+2
B. x^5 - x^3 + 7x^2+2
C. -7x^2 - x^3 + x^5+2
D. 7x^2 + x^3 + x^5+2
Answer:
2 is C. , 3 is C. , 4 is D.
Step-by-step explanation:
2
Square roots are not polynomials
3
The highest degree of one term in the polynomial is 4
4
Terms are separated by (+) or (-) signs. If you count them up there are 4
Answer:
C, D, D, B
Step-by-step explanation:
2. A polynomial has only integer exponents, no square roots. So C is not a polynomial.
3. The degree of the polynomial is the sum of the exponents of the highest term. p has an exponent of 1 and q has an exponent 4, so 1+4 = 5. D
4. Count the number of terms being added or subtracted. p^3, 4pq^2, q^2, and -3q. So there are 4 terms. D
5. Standard form of a polynomial is written from the highest exponent to the lowest. So the answer is B.
how to solve x using logarithms
Step-by-step explanation:
[tex] \frac{1}{2} log(x) + log(4) = 2[/tex]
then
[tex] log( {x}^{ \frac{1}{2} } ) + log(4) = 2 \\ log(4 \sqrt{x} ) = 2 \\ 4 \sqrt{x} = {10}^{2} = 100 \\ \sqrt{x} = 25 \\ x = {25}^{2} = 625[/tex]
I don't know if your Log is natural logarithm then
[tex]4 \sqrt{x} = {e}^{2} \\ \sqrt{x} = \frac{e ^{2} }{4} \\ x = \frac{ {e}^{4} }{16} [/tex]
Simplify the quotient
Answer:
the answer is b
Step-by-step explanation:
What is the y-intercept of the line with a slope of −14 that passes through the point (−2,−92)?
Enter your answer as a number, like this: 42
Or, if your answer is a fraction, such as 314, enter it like this: 3/14
Using the equation of a line as y -y1 = m(x-x1)
Replace m with the given slope and y1 and x1 with the given point:
y - (-92) = -14(x- (-2))
Simpligy:
y + 92 = -14(x +2)
Simplify the right side:
y +92 = -14x -28
Subtract 92 from each side:
y = -14x-120
The y - intercept is -120
Need urgent help, will give brainliest.
A bag has more green balls than blue balls, and there is at least one blue ball. Let b represent the number of blue balls and let g represent the number of green balls. Let's compare the expressions 2b and b+g. Which statement is correct?
A. 2b>b+g
B. 2b
C. 2b=b+g
D. There is not enough information to tell.
The correct comparison for the expressions 2b and b+g is 2b > b+g.
Let's analyze the expressions:
2b: This represents twice the number of blue balls.b+g: This represents the sum of blue balls and green balls.Comparing 2b and b+g, the correct statement is A. 2b > b+g as having more green balls than blue balls implies the total green balls are more, making the expression 2b greater than b+g.
Based on these cases, the only condition that aligns with g > b is when [tex]\(2b < b + g.[/tex]
Thus, the correct answer is: B. 2b < b + g.
To find which statement is correct, let's consider the relationship between the number of green balls (g) and the number of blue balls (b). Since the bag has more green balls than blue balls, it means that g > b.
To compare the expressions 2b and b + g, let's examine their relationship under the condition g > b
When 2b > b + g
Rearranging 2b > b + g, we get:
b > g.
This contradicts the condition g > b.
So, this case is not possible.
Case 2: When 2b < b + g :
Rearranging 2b < b + g, we get:
b < g,
which aligns with the given condition g > b.
Hence, this condition is possible.
When 2b = b + g
Rearranging 2b = b + g, we get: [tex]\[b = g.\][/tex]
This condition contradicts the original requirement g > b, so this case is also not possible.
The only condition that aligns with g > b is when [tex]\(2b < b + g.[/tex] Thus, the correct answer is: B. 2b < b + g.
Question : A bag has more green balls than blue balls, and there is at least one blue ball. Let b represent the number of blue balls and let g represent the number of green balls. Let's compare the expressions 2b and b+g. Which statement is correct?
A. 2b>b+g
B. 2b C. 2b=b+g
D. There is not enough information to tell.
A____is the only parallelogram that can be inscribed in a circle.
Trapezoid
Triangle
Rhombus
Rectangle
Answer:
Rectangle
Step-by-step explanation:
In order for a paralleligram to be inscribed in a circle it has to have four 90º angles, this is why the only parallelogram that can be inscribed into a circle is the rectangle, this includes sqaures, since squares are basically rectangles with equal sides.
(HELP PLEASE)
Describe in your own words the characteristics of linear equations that determine whether a system of linear equations will be Intersecting, Parallel, or Coincident. (2 points, 0.5 for clarity of response, 0.5 for each type of system).
ANSWER
See below
EXPLANATION
Given the system of linear equation:
[tex]y = m_1x + b_1[/tex]
[tex]y = m_2x + b_2[/tex]
If
[tex] m_1 \ne \: m_2[/tex]
then the two equations, will intersect at one. The system has unique solution.
If
[tex]m_1 =m_2 \: and \: b_1 \ne \: b_2[/tex]
then, the two equations are parallel and the system will not have a solution.
If
[tex]m_1 =m_2 \: and \: b_1 = \: b_2[/tex]
Then, the two equations will coincide.
There is infinitely many solutions.
Dayton has 3 bags of frozen vegetables. Each bag has 5/8 pound of vegetables. He plans to make vegetable soup. Each pot of soup takes 1 pound of vegetables
Final answer:
Dayton has 3 bags of frozen vegetables, with each bag weighing 5/8 pound. He can make 1 pot of soup with 7/8 of another pot using these vegetables.
Explanation:
Dayton has 3 bags of frozen vegetables, and each bag contains 5/8 pound of vegetables. To find the total weight of the vegetables, we multiply the weight of one bag by the number of bags: (5/8) * 3 = 15/8 pounds. Since each pot of soup requires 1 pound of vegetables, we divide the total weight of the vegetables by 1 pound to find the number of pots of soup Dayton can make: (15/8) / 1 = 15/8 pots of soup. However, we can simplify this fraction to a mixed number: 15/8 = 1 and 7/8. So Dayton can make 1 pot of soup with 7/8 of another pot.
When solving the equation 12x^2 - 7x = 6-2(x^2 - 1). Evan wrote 12x^2 - 7x = 6 - 2x^2 + 2 as his first step. Which property
justifies this step?
a. subtraction property of equality
b. multiplication property of equality
c. associative property of multiplication
d. distributive property of multiplication over subtraction
Answer:
d. distributive property
Option D is correct, distributive property of multiplication over subtraction is the property used by Evan in first step.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
12x²- 7x = 6-2(x² - 1).
The first step written by Evan is 12x²- 7x = 6-2x² +2
We have to find the property which was used for the first step
In the equation splitted 2(x² - 1) using distributive property of multiplication over subtraction.
The distributive property of multiplication over subtraction is applied when we multiply a value by the difference of two numbers.
Hence, option D is correct, distributive property of multiplication over subtraction is the property used by Evan in first step.
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The sum of the squares of two consecutive odd numbers is 970. Find type integers
Answer:
The two integers you are finding is 21 and 23.
x² + y² = 970
970 / 2 = 485 ( divide it to two because we are finding two integers )
√ 485 = 22.022715546 or when rounded off, 22 ( square root because we are finding squares )
It means, the answers are near the number 22.
I found out 21 and 23
21 and 23 is two consecutive odd integers
Let x = 21
Let y = 23
x² + y² = 970
( 21 )² + ( 23 )² = 970
= 441 + 529
= 970
GIVE ME BRAINLIEST PLEASE !!! :)
Answer:
21, 23 and -21, 23
Step-by-step explanation:
The difference between two consecutive odd numbers is 2.
Let the smaller number be x. Then, the larger number is x + 2.
Now add their squares and set it equal to 970. Then solve for x.
smaller number: x
larger number: x + 2
sum of the squares of the two numbers: x^2 + (x + 2)^2
equation: x^2 + (x + 2)^2 = 970
Solution of the equation:
x^2 + (x + 2)^2 = 970
Expand the square of the binomial:
x^2 + x^2 + 4x + 4 = 970
Combine like terms on the left side:
2x^2 + 4x + 4 = 970
Subtract 970 from both sides:
2x^2 + 4x - 966 = 0
Divide both sides by 2:
x^2 + 2x - 483 = 0
Now we need to factor the binomial. We need two number whose sum is 2 and whose product is -483. Look at 483. It is not divisible by 2, but it is divisible by 3.
483/3 = 161
161 is divisible by 7.
161/7 = 23
23 is prime, so the prime factorization of 483 is
483 = 3 * 7 * 23
Notice that 3 * 7 = 21, so
483 = 21 * 23
Use -21 and 23:
-21 + 23 = 2
-21 * 23 = -483
x^2 + 2x - 483 factors into (x - 21)(x + 23)
Now we continue solving the equation.
x^2 + 2x - 483 = 0
(x - 21)(x + 23) = 0
x - 21 = 0 or x + 23 = 0
x = 21 or x = -23
We let x equal the smaller of the two integers, so now we add 2 to find the second integer.
x = 21; x + 2 = 23
x = -23; x + 2 = -21
There are two sets of consecutive odd numbers that satisfy this problem.
21, 23
-23, -21
The problem did not state positive or negative consecutive odd numbers, so both solutions are valid.
Which distribution is likely to have a mean higher than the median?
Answer:
A distribution that is skewed to the right is likely to have a mean higher than the median.
Can I get help on this also plz? I need a step by step explanation. Thank you so much!
Answer:
5) x=30
6) x=50
7) x=59
8) x=31
9) m<1=75 because they're corresponding and m<2=105 because it's supplementary with the 75 degrees angle
10) m<1= 120 because they're corresponding and m<2=60 because they're consecutive interior angles and add up to 180
in questions 5-7 you just set them equal to each other
in 8, you had to subtract 105 from 180 and then set 75 equal to 3x-18
The sequence below is arithmetic:
{1, 8, 27, 64}
True
False
The sequence {1, 8, 27, 64} is not an arithmetic sequence.
An arithmetic sequence is defined by having a constant difference between consecutive terms. To check if a sequence is arithmetic, we subtract each term from the one that follows.
The difference between 8 and 1 is 7
(8 - 1 = 7)
The difference between 27 and 8 is 19
(27 - 8 = 19)
The difference between 64 and 27 is 37
(64 - 27 = 37)
Since these differences are not equal, the sequence is not arithmetic.
A scientist has a data set consisting of the temperature at which a chemical solution begins to evaporate. There are 500 measurements in the data set. He plans to estimate the standard error for the mean temperature by drawing a random sample from the data set consisting of 64 measurements.
What formula would produce an estimate for the standard error of the sample?
Divide the sum of all the measures by 500.
Divide the standard deviation of the sample measures by 8
Divide the sum of the sample measurements by 64
Calculate the sum of the squares of the deviations of the sample
Answer:
Divide the standard deviation of the sample measures by 8
Step-by-step explanation:
Given
measurements in data set=500
measurements in sample=64
Standard error of sample=?
As per the formula of standard error
Standard error= standard deviation/ square root of the number of measurements
= σ/√n
Here as we need to find standard error of the sample hence n=64
therefore √64= 8
The above equation will become:
standard error of the sample= σ/8 i.e. Divide the standard deviation of the sample measures by 8!
Please help me I'm sooooo stressed!!!! plz help
Answer:
with what you didnt say what you needed help with
Step-by-step explanation:
Jason is trying to prove that this quadrilateral is a rhombus. Using the slope formula, he finds that opposite sides of the polygon are parallel. Since all of the sides appear to be congruent, Jason concludes that ABCD is a rhombus. Is Jason's reasoning correct? Why or why not?
Answer:
incorrect; Jason must also prove that all sides are congruent by using the distance formula.
Step-by-step:
By definition, a rhombus has two pair of parallel sides and all sides are congruent. Jason must use the distance formula in a formal algebraic proof to prove that all sides are congruent. Just looking at the graph is not sufficient proof.