Answer:
A complex number is of type
a+bi
where a is the real parts and b is the imaginary part.
Step-by-step explanation:
A complex number is of type
a+bi
where a is the real parts and b is the imaginary part.
i is called imaginary number because no real number satisfies this equation
An example of complex number can be: 7+8i or 23+9i etc
What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?
For this case we have that by definition, the Greatest Common Factor (GCF) is the largest factor that 2 numbers have in common.
So, we have the following expressions:
[tex]42a ^ 5b ^ 3\\35a ^ 3b ^ 4\\42ab ^ 4[/tex]
We look for the positive integers that divide to 35 and 42 without leaving residue:
42: 1,2,3,6,7,14,21
35: 1,5,7
Thus, the GCF of 42 and 35 is 7
Then, the GCF of the three expressions is:
[tex]7ab ^ 3[/tex]
Answer:
[tex]7ab ^ 3[/tex]
Answer:
A) 7ab^3
Step-by-step explanation:
EDG2021
A patient takes a medication with a half life. Initially, there are 20 milligrams of the medication in the patient's system. After 8 hours there are 12 milligrams. How many milligrams will there be after 10 hours? Round your answer to the nearest hundredth, and do not include units
Answer:
At 10 hours there will be 10 milligrams
Step-by-step explanation:
On a graph your slope would be y= -1x+20 because there where 20 mill at 0 hours and 12 mill at 8 hours. 20-8=12 meaning 1 mill would be deluded every hour. Hope this helps.
Final answer:
Using the exponential decay formula, we can find the half-life of the medication from the initial and given 8-hour amounts and then use it to calculate the amount of medication remaining after 10 hours.
Explanation:
To determine the remaining medication after a given number of hours, we will apply the exponential decay formula which accounts for substances with a half-life. Thus, given that there are initially 20 milligrams of the medication and that it decreases to 12 milligrams after 8 hours, we need to calculate the half-life and then use it to predict the amount remaining after 10 hours.
First, finding the half-life 't1/2' can be done using the formula A = A0×2−t/t1/2, where A is the remaining amount (12 mg), A0 is the initial amount (20 mg), and t is the time elapsed (8 hours). Solving for the half-life gives us t1/2 as the unknown in this equation.
12 mg = 20 mg ×2−(8 hours)/t1/2
Reducing this equation, we find that:
t1/2 = 8 hours / (log2(20 mg/12 mg))
After finding 't1/2', we can then determine the amount remaining after 10 hours. The calculation would be as follows:
A = 20 mg ×2−(10 hours)/t1/2
This will give us the final amount of medication left in the system at the 10-hour mark, rounded to the nearest hundredth.
Find the indicated term of the given geometric sequence.
a = 14, r = –2, n = 11
Answer:
-14336
Step-by-step explanation:
We are given the first term (a) = 14, the common ratio (r) = -2 and the number of term (n) = 11 that we are to find for a geometric sequence.
We know that the formula of nth term for a geometric sequence is given by:
[tex]n^{th}term = ar^{n-1}[/tex]
Substituting the given values in the above formula to find the 11th term:
11th term = [tex] 14 \times 2^{11-1}[/tex] = -14336
What is the square root of 16x^
36?
Note that [tex]\sqrt[2]{x}=x^{\frac{1}{2}}[/tex]
[tex]\sqrt[2]{16x^{36}}=\sqrt[2]{4^2x^{18\cdot2}}[/tex]
[tex]4^{2\cdot\frac{1}{2}}x^{18\cdot2\cdot\frac{1}{2}}=4^{\frac{2}{2}}x^{\frac{18\cdot2}{2}}[/tex]
[tex]\boxed{4x^{18}}[/tex]
Hope this helps.
r3t40
The polynomial (x - 2) is a factor of the polynomial 4x2 - 6x-4. True or false?
Solve h2-42 = -h using the quadratic formula.
A) h = 0 or h = 7
B) h = -6 or h = 7
C) h = 6 or h= -7
D) h = -6 or h = -7
Answer: Option C
h = 6 or h= -7
Step-by-step explanation:
We have the expression
[tex]h^2-42 = -h[/tex]
To solve add h on both sides of the equality
[tex]h^2+h-42 = -h+h[/tex]
[tex]h^2+h-42 = 0[/tex]
For an equation of the form [tex]ah^2 +bh +c[/tex] the quadratic formula is
[tex]h=\frac{-b \± \sqrt{b^2 -4ac}}{2a}[/tex]
In this case
[tex]a = 1\\b= 1\\c =-42[/tex]
[tex]h=\frac{-1 \± \sqrt{1^2 -4(1)(-42)}}{2(1)}[/tex]
[tex]h_1=6[/tex]
[tex]h_2=-7[/tex]
The answer is the option C
Which of the following sets are continuous?
Answer:
A, C and D are continuous
Step-by-step explanation:
A is a set of any number x which 30 < x <=45
B is a set that contains only 3 and 7
C is a set of any number x which 60 <= x < 100
D is a set of any number x which -infinity < x < + infinity
E is a set that contains only even whole numbers
A continuous data set is a quantitative data set representing a scale of measurement that can consist of numbers other than whole number, like decimals and fractions.
Step by step If C(m)=0.50m + 30 represents the cost of renting a car, how many miles were driven if the cost is $130
Answer:
200 miles were driven
Step-by-step explanation:
We know that [tex]C (m) = 0.50m + 30[/tex] represents the cost of renting a car
Where m represents the number of miles driven
If we know that the cost was $ 130 then we can equal C(m) to 130 and solve for m.
[tex]C(m) =0.50m + 30=130[/tex]
[tex]0.50m + 30=130[/tex]
[tex]0.50m=130-30[/tex]
[tex]0.50m=100[/tex]
[tex]m=\frac{100}{0.50}[/tex]
[tex]m=200\ miles[/tex]
Name the property: 3x(4x5)=(3x4)x5
Answer:
Commutative Property because it only switched the numbers around.
The property represented by the equation 3x(4x5)=(3x4)x5 is the Associative Property of Multiplication, which indicates that numbers' grouping does not influence the outcome of multiplication.
Explanation:The property represented by the equation 3x(4x5)=(3x4)x5 is called the Associative Property of Multiplication. This property states that the way in which numbers are grouped when being multiplied does not change the product. In your equation, whether you multiply 4 and 5 first (in the expression 3x(4x5)) or 3 and 4 first (in the expression (3x4)x5), the result is the same.
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Which of the following is the conjugate of the expression below when x> -3?
7- square root of x+3
Answer:
[tex]7+\sqrt{x+3}[/tex]
Step-by-step explanation:
The conjugate of a radical expression is obtained by changing the sign of the middle term.
The conjugate of [tex]a+\sqrt{b}[/tex] is simply [tex]a-\sqrt{b}[/tex]
Therefore, to obtain the conjugate of the given expression we simply shall be changing the negative sign to positive;
The conjugate of [tex]7-\sqrt{x+3}[/tex] is simply;
[tex]7+\sqrt{x+3}[/tex]
What is the output of the following function for x 1? F(x)=-x^3-2x^2+7x-10
Answer:
-6
Step-by-step explanation:
Let x =1
F(x)=-x^3-2x^2+7x-10
F(1) = - (1)^3 -2(1)^2 +7(1) -10
= -1 -2 +7-10
= -3+7-10
=-6
The output of the given function F(x)=-x^3-2x^2+7x-10 when x equals 1 is -6. We substituted x=1 into each term to calculate this.
Explanation:The given function is F(x)=-x^3-2x^2+7x-10. To find the output of the function when x equals 1, you substitute '1' in place of 'x' in the equation. So let's calculate:
For -x^3, substituting x=1, we get: -1^3 = -1For -2x^2, substituting x=1, we get: -2*(1^2) = -2For 7x, substituting x=1, we get: 7*1 = 7Lastly, -10 remains the same as there's no x to substituteNow, add all the results together: -1 - 2 + 7 - 10 = -6. Therefore, when x equals 1, the output of the function F(x) is -6.
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Kira walks 8 and a half blocks in 17 minutes. If Kira continues to walk at a steady pace, how many blocks will she walk each minute
Answer:
Half a block ( 0.5 or 1/2 )
Step-by-step explanation:
8 1/2 blocks can also be written as 8.5 blocks.
If Kira walks 8.5 blocks in 17 minutes [and continues to walk at this steady pace], divide 8.5 by 17.
8.5/17 = 0.5
So, Kira walked 0.5 or 1/2 blocks in a minute.
I hope this helps! :)
Kira walks at a rate of 0.5 blocks per minute when she walks 8 and a half blocks in 17 minutes.
Kira walks 8 and a half blocks in 17 minutes. To find out how many blocks she will walk each minute, we need to calculate the rate by dividing the total number of blocks by the total number of minutes:
Rate = Total Blocks Walked / Total Minutes
Rate = 8.5 blocks / 17 minutes
Rate = 0.5 blocks per minute.
Therefore, at a steady pace, Kira will walk half a block every minute.
Solve the equation:
5 - 20 =
– 15
Enter answer below
Enter your response
Answer:
15
Step-by-step explanation:
First add 20 to both sides to get x/3 = 5
Then multiply both sides by 3 to get 15.
You can check it by substituting it into the equation
15/3 - 20 = -15
5 - 20 = -15
-15 = -15
Step-by-step explanation:
x/3 - 20 = -15
x/3 = -15 + 20
x/3 = 5
x = 15
A car race lasted 2.07 hours. How many seconds did the race last? If
necessary, round your answer to the nearest tenth of a second.
1 hour = 60 minutes
1 minute = 60 seconds
therefore 2.07 hours = (2.07*60*60) seconds
=7452 seconds
Answer:
7452
Step-by-step explanation:
There are 3600 seconds per hour
60*60= 3600
To find how many seconds are in 2.07 hours you need to multiply 3600 by 2.07
2.07* 3600 = 7452 seconds
Hope This helps
What is the domain of the function y= x + 6 - 7
Answer:
x is in the element of all real numbers.
Step-by-step explanation:
Simplify the equation.
[tex]y=x+6-7[/tex]
[tex]y=x-1[/tex]
This means that the equation [tex]y=x[/tex] has just been moved down one.
Since the equation can be any number on the x axis, the domain is all real numbers.
Answer: X is all numbers I think.
Step-by-step explanation:
Solve the following system of equations using the substitution method.
-X + 9y = -5
x - 5y = 1
Answer: x=8.5 y=1.5
Step-by-step explanation:
Use the second problem and get X by itself. X= 5y+1. Now plug that equation into the 1st equation.
-(5y+1) +9y =-5.
-5y-1+9y=-5.
-5y+9y= 1+5
4y= 6
Y=1.5
Now that you know what is the value of Y you can plug that into any equation.
5(1.5) +1
7.5+1
X=8.5
For this case we have the following system of equations:
[tex]-x + 9y = -5\\x-5y = 1[/tex]
We clear "x" from the second equation and replace it in the first:
[tex]x = 1 + 5y[/tex]
Substituting in the first equation:
[tex]- (1 + 5y) + 9y = -5\\-1-5y + 9y = -5[/tex]
We have similar terms:
[tex]-1 + 4y = -5[/tex]
Adding 1 to both sides of the equation:
[tex]4y = -5 + 1\\4y = -4\\y = \frac {-4} {4}\\y = -1[/tex]
We look for the value of "x":
[tex]x = 1 + 5 (-1)\\x = 1-5\\x = -4[/tex]
Answer:
[tex](x, y): (- 4, -1)[/tex]
which of the following equations is of a parabola with a vertex at (1,2)
answer choices
1. y=(x-1)^2 - 2
2 . y=(x-1)^ 2 + 2
3 . y=(x+1)^2 - 2
4 . y=(x+1)^2 + 2
ANSWER
The choice is correct.
[tex]y = {(x -1)}^{2} + 2[/tex]
EXPLANATION
The equation of a parabola in vertex form is given by:
[tex]y = a {(x -h)}^{2} + k[/tex]
where (h,k) is vertex of the parabola and 'a' is the leading coefficient of the parabola.
From the given options, the leading coefficient must be a=1.
We also have the vertex of the parabola at (1,2). This implies that h=1 and k=2.
We substitute these values into the formula to get,
[tex]y = {(x -1)}^{2} + 2[/tex]
The second option is correct.
In 2014, there were approximately 900,000 sworn law enforcement officers serving in the U.S. Approximately 12% of those officers were female. How many officers were females?
Answer:
108,000 females
Step-by-step explanation:
12% of 900,000 is 108,000.
Therefore, there are 108,000 female officers in the U.S.
Answer: 108,000
Step-by-step explanation:
In 2014, 900,000 sworn law enforcement officers who were serving in the United States and 12% of those officers were female. To find the number of females that were law enforcement officers, we multiply the percentage of females by the total number of law enforcement officers. This will be:
= 12% of 900000
= 12/100 × 900000
= 0.12 × 900000
= 108,000
There were 108,000 females as law enforcement officers serving in the United States.
a right prism has a square base, a surface area of 512 inches squared, and a height of 12 inches. Find the length of the square base
Answer:
8 inches
Step-by-step explanation:
Surface area of a prism is:
S = 2A + Ph
where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.
The base is a square, so A = s² and P = 4s:
S = 2s² + 4sh
Given that S = 512 and h = 12:
512 = 2s² + 4s(12)
512 = 2s² + 48s
256 = s² + 24s
0 = s² + 24s - 256
0 = (s + 32) (s - 8)
s = -32, s = 8
Since s must be positive, s = 8 inches.
Follow below steps;
To find the length of the square base of the right prism:
First, calculate the lateral surface area: 512 in² = 4s * 12 where s is the side length of the square base.
Then, solve for s: 512 = 48s, s = 512 / 48 = 10.67 in.
Therefore, the length of the square base is 10.67 inches.
What is the length of diameter EF?
3
6
9
Answer:
6
Step-by-step explanation:
You are given the radius, 3
The diameter is twice the radius, so 6.
find the prime factorization of following the number: 56
Answer:
2×2×2×7=56
Step-by-step explanation:
Find the multiples that goes into 56
Each number that goes into 56 put then from least to greatest and you got your prime numbers
Two lines, A and B, are represented by the following equations: Line A: 4x + 4y = 16 Line B: x + y = 4 Which statement is true about the solution to the set of equations?
Answer:
The set of equations has an infinite number of solutions
Step-by-step explanation:
The system of linear equations represented by the following equations:
Line A: 4x + 4y = 16 and Line B: x + y = 4 are dependent.
This is because both equations represent the same line;
if we divide both sides of the equation of line A by 4, we would obtain
x + y = 4, which is basically the equation of line B
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
A rectangular field is 3 times as long as it is wide,
and it has an area of 192 square yards. How many
yards long is it?
It is 24 yards long.
Let the width = x
Given that the rectangular field is 3 times as long as it is wide.
So, the length = 3x.
So area = Length * width = [tex](3x)*(x) = 3x^2[/tex].
Given: it has an area of 192 square yards.
So,
[tex]3x^2=192\\x^2=64\\x=\sqrt{64}\\x=8[/tex]
So length = 3x = 3(8) = 24.
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To the nearest hundredth of a centimeter, what is the length of a leg of the triangle?
[1] cm
84.6 cm
Answer:
The length of a leg of the triangle = 59.83 cm
Step-by-step explanation:
Points to remember
If a right angled triangle with angles 45°, 45° and 90° then the sides are in ratio 1 : 1 : √2
It is given a right angled triangle with 45°, 45° and 90° and hypotenuse = 84.6 cm
To find the length of a leg
Let 'x' be the length of each leg,
From the figure we can write,
1: 1 : √2 = x : x : 84.6
Therefore x = 84.6/√2
= 59.83 cm
Therefore the length of a leg of the triangle = 59.83 cm
ANSWER
59.82
EXPLANATION
The given right angle is an isosceles right triangle.
Let the length of a leg be x cm.
Then by the Pythagoras Theorem,
[tex] {x}^{2} + {x}^{2} = 84.6 ^{2} [/tex]
[tex]2 {x}^{2} = 7157.16[/tex]
Divide both sides by 2.
[tex]{x}^{2} = \frac{7157.16}{2} [/tex]
[tex]{x}^{2} = 3578.58[/tex]
Take positive square root of both sides to get,
[tex]x = 59.82123369[/tex]
Hence the length of a leg is 59.82 to the nearest hundredth.
help me help me plsss
60 points
-75 = -8b - 7b
To solve for "b" you must isolate it, meaning that "b" must be the only thing on the right side of the equation.
First you must combine like terms. Like terms are numbers that have matching variables OR are numbers with out variables. In this case the like terms are -8b and -7b, since they both have the variables "b" attached.
-8b + (-7b) = -15b
so...
-75 = -15b
Next, to completely isolate b, divide -15 to both sides. Since -15 is being multiplied by b, division (the opposite of multiplication) will cancel -15 out (in this case it will make -15 one) from the right side and bring it over to the left side.
-75/-15 = -15b/-15
5 = 1b
b = 5
Check:
-75 = -8(5) - 7(5)
-75 = -40 - 35
-75 = -75
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
8b is the answer to this question.
Step-by-step explanation:
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function? The domain is all real numbers. The range is {y|y < 16}. The domain is all real numbers. The range is {y|y ≤ 16}. The domain is {x|–5 < x < 3}. The range is {y|y < 16}. The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}.
Answer:
The domain is all real numbers. The range is {y|y ≤ 16}
Step-by-step explanation:
we have
[tex]f(x)=-x^{2}-2x+15[/tex]
This is a the equation of a vertical parabola open downward
The vertex is a maximum
The vertex is the point (-1,16)
see the attached figure
therefore
The domain of the function is all real numbers ----> interval (-∞,∞)
Te range of the function is
[tex]y\leq 16[/tex]
All real numbers less than or equal to 16 ----> interval (-∞,16]
Answer:b
Step-by-step explanation:
When is a lower annual interest fee better than a low annual fee
Answer: a lower annual interest fee is better than a low annual fee if you expect to pay your balance in full during most months
Final answer:
A lower annual interest fee is generally better than a low annual fee when it leads to significant savings over time, especially with large amounts or long-term financial products. Interest rates dictate the overall cost of borrowing more than annual fees, particularly for longer terms or larger sums. However, for small, short-term borrowing, a low annual fee might be more beneficial.
Explanation:
When comparing a lower annual interest rate versus a low annual fee, it is essential to consider the specific financial situation and the amount of money involved. As a general rule, a lower interest rate is beneficial when it leads to significant savings on the overall interest paid throughout the loan or credit product term. This is often the case for larger amounts or longer terms where the interest accumulates considerably over time.
For example, financial investors who choose a Certificate of Deposit (CD) earn a higher interest rate compared to savings accounts, as they agree to leave the money deposited for a fixed period, forgoing liquidity. However, if interest rates rise after a loan is made, the existing loan with the lower interest rates becomes less attractive. On the other hand, if the economy experiences a fall in interest rates, the value of the loan with the previously fixed lower rate increases.
Therefore, while a low annual fee can seem attractive, it's the annual interest that ultimately has a more significant impact on the cost of borrowing, especially over longer periods or with larger sums of money. Conversely, for small short-term loans or when the outstanding balance is frequently paid off, a low annual fee might be more advantageous than a lower interest rate, as the interest charges could be minimal.
please help Solve (x-5)^2=3
Answer:
x = 5 + √3, 5 - √3
which is 6.73 , 3.27 to the nearest hundredth.
Step-by-step explanation:
(x - 5)^2 = 3
Take the square root of both sides:
x - 5 = +/- √3
x = 5 + √3, 5 - √3
Answer:
x = 5 + √3 or x = 5 - √3
Step-by-step explanation:
Equation: (x - 5)² = 3
Square root: x - 5 = ±√3 <-- the square root of a number can be positive or negative.
Subtract: x = 5 + √3 or x = 5 - √3
Use the quadratic function to predict f(x) if x equals 8.
f(x) = 25x2 − 28x + 585
Answer:
1961
Step-by-step explanation:
replace x with 8
25(8)^2-28(8)+585
25(64)-28(8)+585
1600-224+585
1961
f(8) = 1961.
The quadratic function given is: f(x) = 25x2 - 28x + 585
To predict f(x) when x = 8:
Substitute x = 8 into the function:
f(8) = 25(8)2 - 28(8) + 585
f(8) = 25(64) - 224 + 585
f(8) = 1600 - 224 + 585
f(8) = 1961
Therefore, f(8) equals 1961.
What is the solution to the following equation?
X+(-13) = -5
The answer is -65
X+(-13)=-5
x=13*-5
13 * -5= -65
x=65
An equation is formed when two equal expressions. The solution of the equation x+(-13) = -5 is 8.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the equation x+(-13) = -5 is,
x + (-13) = -5
x - 13 = -5
x = -5 + 13
x = 8
Hence, The solution of the equation x+(-13) = -5 is 8.
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