Answer:
The factor form of given expression is (x-4)(x-2i)(x+2i).
Step-by-step explanation:
The given expression is
[tex]x^3-4x^2+4x-16[/tex]
It can be written as
[tex]f(x)=x^3-4x^2+4x-16[/tex]
According to the rational root theorem, all possible rational roots are in the form of
[tex]\frac{a_0}{a_n}[/tex]
Where, a₀ is constant term and [tex]a_n[/tex] is leading coefficient.
[tex]f(4)=4^3-4(4)^2+4(4)-16=0[/tex]
Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.
Use synthetic method to find the remaining factors.
[tex](x^3-4x^2+4x-16)=(x-4)(x^2+4)[/tex]
[tex](x^3-4x^2+4x-16)=(x-4)(x^2-(2i)^2)[/tex]
[tex](x^3-4x^2+4x-16)=(x-4)(x-2i)(x+2i)[/tex]
Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).
Answer:
(x-4) (x-2i) (x+2i)
Step-by-step explanation:
x^3−4x^2+4x−16
I will factor by grouping
x^3−4x^2+ 4x−16
The first group is the first 2 terms. I can factor out an x^2
x^2 (x-4) + 4x-16
The second group I can factor out a 4
x^2 (x-4) + 4(x-4)
Now I can factor out (x-4)
(x-4) (x^2 +4)
We know that x^2 + 4 factors into +2i and -2i because
(a^2 -b^2) = (a-b) (a+b) but we have (a^2 + b^2) = (a-bi) (a+bi)
(x-4) (x-2i) (x+2i)
Select the multiplication sentence that applies the associative property of multiplication to the example. Example: (5 × 3) × 2 = 30 A. (5 + 3) × 2 = 16 B. 5 × (3 + 2) = 25 C. 5 × (3 × 2) = 30 D. 2 + (4 × 7) = 30
Answer : C
A. (5 + 3) × 2 = 16
Here we have 5 +3 . there is a + sign in between. so it does not comes under Associative property of multiplication
B. 5 × (3 + 2) = 25
We have 3 + 2 . there is a + sign in between. so it does not comes under Associative property of multiplication
C. 5 × (3 × 2) = 30
we have 5 times 3 times 2. so it comes under Associative property of multiplication
D. 2 + (4 × 7) = 30
We have 2 + . there is a + sign in between. so it does not comes under Associative property of multiplication
X to the power of 2 equal 100 how to solve
Answer: {-10, +10}
Step-by-step explanation: A common mistake in this problem would be to say that if x² = 100, x must equal 10.
Remember however that before you do anything else you must set the equation equal to 0.
So our first step is to subtract 100 from both sides to get x² - 100 = 0. Next, factor the left side to get (x + 10)(x - 10) = 0.
So either x + 10 = 0 or x - 10 = 0.
Solving for x in each equation, we have x = -10 or x = +10.
So our answer is not just 10, it's -10 or +10.
I have also attached my work in the image provided.
Use the complex conjugate to find the absolute value of 8+12i
A. 12
B.Square root of 208
C. Square root of 84
D. 8
Answer:
A. 12
Step-by-step explanation:
i= use complicated conjugate to search out definite quantity of 8 + 12i
i = 12i
i= twelve × ei 90°
i = twelve × (cos 90° + i sin 90°)
r = |i| = twelve
The absolute value of the complex number 8 + 12i is found by squaring the real part, squaring the imaginary part, adding these two results, and then taking the square root. This results in the square root of 208.
Explanation:The absolute value of a complex number a + bi is calculated through the formula sqrt(a² + b²). So, to find the absolute value of the complex number 8 + 12i, we substitute a with 8 and b with 12. We can perform the calculations as follows:
Square the real part, a: 8² = 64,Square the imaginary part, b: 12² = 144,Add the results: 64 + 144 = 208,Take the square root of the sum: sqrt(208). Thus, the absolute value is the square root of 208.Learn more about Complex Numbers here:https://brainly.com/question/20566728
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Which best describes the association between variables x and y?
A. Strong Positive
B. Strong Negative
C. Weak Positive
D. Weak Negative
Answer: C. Weak Positive
Step-by-step explanation:
In a scatter plot , a positive correlation is a relationship between the two variables x and y in which if value at x axis increases, then other value at y axis also increases.
In the given scatter plot the the association between variables x and y is a weak positive correlation because there is a lower likelihood in the relationship between variables.
WILL GIVE BRAINLIEST!!! PLEASE HELP!
write a mathematical equation stating that three consecutive even integers add up four times the smallest
PLEASE HELP!!!!!!!!!!!!!!!
Hey there!!
Let's take the first number an the smallest number as ' x '
Then, the second consecutive even integer would become ' x + 2 '
Third integer ' x + 4 '
Hence, adding them up, we get,
x + x + 2 + x + 4
... 3x + 6
This is equal to 4 times the smallest number.
We got the smallest number as ' x '
Hence, the final equation :
... 3x + 6 = 4x
Hope my answer helps!!
Ms.Omalley's cousin lives 1,650 miles away.Ms.Omalley's won a gift card for 100 gallons of gas.If her car can travel 35 miles on each gallon,can she do a roundtrip to see her cousin on the free gas? Explain how you know.
Julia rounded to the nearest ten to estimate the difference between two numbers. The estimated difference was 10. What are four pairs of numbers she might have sustractrd?
To round off to 10, the difference should range from 5 to 14. If the difference between two numbers is from 5 to 14, they all are rounded to 10.
Example:
[tex]18-9=9[/tex] (near to 10)
[tex]26-15=11[/tex]
[tex]46-39=7[/tex]
[tex]50-42=8[/tex]
If Julia rounded to the nearest ten to estimate the difference between two numbers. The estimated difference was 10. (18,9)(25,14), (36,22) and (45, 38) are few pairs of numbers she might have subtracted.
What is Number system?A number system is defined as a system of writing to express numbers.
The difference should range from 5 to 14.
Difference in math is the result of one of the important mathematical operations, which is obtained by subtracting two numbers
To round off to 10.
If the range of difference between two numbers is from 5 to 14. Then those numbers are rounded to ten.
Let us consider some pairs of numbers whose difference is rounded to ten.
18-9=9
25-14=11
36-22=14
45-38=7
Hence (18,9)(25,14), (36,22) and (45, 38) are few pairs of numbers she might have subtracted.
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The average height of a female giraffe is4.6 meters What is her height in centimeters
460 cm
note that 1m = 100 cm, thus
4.6m = 4.6 × 100 = 460 cm
Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year. Write an equation to model the car's value.
y=20,000-.10x
with x being the number of years
Answer:
[tex]y=\$20,000\cdot (0.90)^x[/tex]
Step-by-step explanation:
We have been given that Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year. We are asked to write an equation to model the car's value.
Since car's value depreciates by 10% per year, so value of car is depreciating exponentially.
We know that an exponential decay function is in form [tex]y=a\cdot (1-r)^x[/tex], where
a = Initial value,
r = Decay rate in decimal form.
Let us convert 10% into decimal form as:
[tex]10\%=\frac{10}{100}=0.10[/tex]
Upon substituting our given values in decay formula, we will get:
[tex]y=\$20,000\cdot (1-0.10)^x[/tex]
[tex]y=\$20,000\cdot (0.90)^x[/tex]
Therefore, our required equation would be [tex]y=\$20,000\cdot (0.90)^x[/tex].
3. At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount, but each was $2.25 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items?
(a) Write an equation. Let x represent the cost of one of Tanya's items.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.
By setting up an equation with x as the cost of Tanya's items, we find that each of Tanya's items cost $9.00. Tony's items, being $2.25 cheaper, cost $6.75 each. The solution is checked by ensuring both Tanya's and Tony's total expenditure was equal.
The question asks us to find the individual cost of items purchased by Tanya and Tony at a store, given that Tony's items each cost $2.25 less than Tanya's but both spent the same amount overall.
Equation Setup
Let x represent the cost of one of Tanya's items. Since Tanya bought 3 items, she spent 3x dollars. Tony's items each cost $2.25 less, so they cost (x - $2.25) each. Tony bought 4 items, spending 4(x - $2.25). Since both spent the same amount:
3x = 4(x - $2.25)
Solving the Equation
To solve for x:
Distribute the 4 on the right side of the equation to get 3x = 4x - $9.00.Subtract 4x from both sides to get -x = -$9.00.Divide both sides by -1 to get x = $9.00.So, each of Tanya's items cost $9.00.
Checking the Solution
To verify:
Tanya's total is 3($9.00) = $27.00.Tony's total is 4($9.00 - $2.25) = 4($6.75) = $27.00.Both totals match, confirming that the solution is correct.
Tanya's items each cost $9.00, while Tony's items, costing $2.25 less, each cost $6.75.
$1,200 is invested in an account earning 6.5% interest compounded annually. How much will there be in the account after 3 years?
Answer:
B. $1,449.54
Step-by-step explanation:
That's the answer
Alonzo's gas tank is 1/3 full. After he buys 3 gallons of gas, it is 1/2 full. How many gallons can Alonzo's tank hold?
Find the sum of the first 4 terms of the series.
2-8+32-128+...
a. –101
c. –102
b. –103
d. –104
The sum of the first four terms of the series would be c. -102
1.819÷1.2 round your answer to the nearest tenth
What is the remainder of 23870 divide by 38
The remainder when dividing 23870 by 38 is 16.
Explanation:To find the remainder when dividing 23870 by 38, you divide the larger number (the dividend) by the smaller number (the divisor). If the division operation does not produce a whole number, the 'left over' digits are considered the remainder. When you divide 23870 by 38, the quotient (or the answer) is 628, and the remainder is 16. Therefore, 16 is the remainder when 23870 is divided by 38.
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15 points all other rewards will be given please no non-scene
uoy knaht
Consider these three numbers written in scientific notation.
1.67 x 10-4
9.7 x 10-6
4.5 x10-9
Which shows the numbers in order from least to greatest?
A.
1.67 x 10-4 ,
9.7 x 10-6,
4.5 x 10 -9
B.
4.5 x 10-9,
9.7 x 10-6 ,
1.67 x 10 -4
C. 1.67 x10 -4 ,
4.5 x 10-9 ,
9.7 x 10-6
D. 9.7 x 10-6 ,
4.5 x 10-9,
1.67 x 10-4
Why hello there
The correct answer is B
If my answer helped please mark me as brainliest thank you and have the best day ever!
What are the discontinuities of the function f(x) = the quantity x squared minus 36 over the quantity 4x plus 24?
there is a point discontinuity ( hole ) at (- 6, - 3 )
factor the numerator/denominator
f(x) = [tex]\frac{(x-6)(x+6)}{4(x+6)}[/tex]
the factor (x + 6) cancels leaving the simplified version of f(x)
f(x) = [tex]\frac{x-6}{4}[/tex]
the removal of the factor (x + 6) from the numerator/denominator means there is a discontinuity at x + 6 = 0 , that is x = - 6
f(- 6 ) = [tex]\frac{-6-6}{4}[/tex] = - 3
there is a point discontinuity ( hole ) at (- 6, - 3 )
Allen score in the video game was changed by -75 points because he miss some targets he got -15 points for each miss target how many targets did he miss
Answer:
he missed 5 targets
Step-by-step explanation:
What is the correct evaluation of 2a2 - 3b2 when a is equal to 2 and b is equal to -1?
A.11
B.5
C.-5
D.-11
The correct answer is A. 11
There are 87.4 calories in one serving of cherries. How many calories are in 3.85 servings?
Answer:
336.49 calories.
Step-by-step explanation:
if; 87.4 calories = 1 serving of cherries
so; how much calories = 3.85 serving of cherries
hence:
3.85 seving * 87.4 calories / 1 serving
the answer is
336.49 calories
5. Solve the inequality. Show your work. 5y + 16 ≤ 56-
Answer: y ≤ 8
Solution:
Step 1: Rearrange the equation so that all the like terms are on one side
5y + 16 ≤ 56
= 5y ≤ 56 - 16 constants on one side and variable on the other
= 5y ≤ 40
= y ≤ 8
Hope the solution helps to understand the question!
Tip: Remember that if the inequality is multiplied by a negative sign the inequality sign flips.
3( x -5)- 5x= 25+ 6x What is the answer and how do you solve this??
To solve this equation, distribute, combine like terms, and isolate the variable, x.
Explanation:To solve this equation, we need to simplify both sides and isolate the variable, x.
Starting with the left side, distribute the 3 to the terms inside the parentheses: 3x - 15 - 5x = 25 + 6x.
Combine like terms on both sides of the equation: -2x - 15 = 25 + 6x.
Add 2x to both sides of the equation and add 15 to both sides: -15 - 25 = 6x + 2x.
Simplify the equation: -40 = 8x.
Finally, divide both sides by 8 to solve for x: x = -5.
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a boat is marked up to 20% on the original price . The original price was $50 what is the sales price of the boat before sales tax?
Answer:
60
Step-by-step explanation:
Answer:
60 dollars.
Step-by-step explanation:
Markup is nothing but the difference between the selling price of a good or service and its cost. It is expressed as a percentage above the cost. In short, we can say that it is the added price over the total cost of the good or service that provides the seller with a profit.
Original price = 50 dollars
ADD: 20% on original price = Markup price = 50(20/100) = 10 dollars
Hence Sales price = 50+10 = 60 dollars
Kate sets a goal to walk 3 miles every day for a year. How many miles more or less than 1,000 miles will she walk in the year? A. 33 miles less B. 95 miles more C. 33 miles more D. 95 miles less
3 miles per day * 365 days = 1095
1095-1000=95
The answer is B. 95 miles more.
Find the area of the rectangle 9ft and 14ft
You simply need to mulotiply those two numbers
Then u get 126!
Easy Peasy
Find two consecutive positive integers such that the sum of their squares is 841
Let x = 1st positive integer
Let x + 1 = 2nd positive integer
As give, their sum of squares is 841
[tex]x^{2}+(x+1)^{2}=841[/tex]
[tex]x^{2}+x^{2}+2x+1=841[/tex]
[tex]2x^{2}+2x+1=841[/tex]
[tex]2x^{2}+2x-840=0[/tex]
factor 2 out, [tex]x^{2}+x-420=0[/tex]
[tex]x^{2}+21x-20x-420=0[/tex]
[tex]x(x+21)-20(x+21)=0[/tex]
(x+21)(x-20)
This gives, x=20 and =-21 (neglect the negative value)
So, x = 20
x+1 = 21
So, the two numbers are : 20 and 21
Find the perimeter of a triangle garden that measures 10 feet by x feet by (2 x+7) feet . Use p=a+b+c
P = 10 + x + 2x + 7
= (10 + 7) + (x + 2x)
= 17 + 3x
Therefore, the perimeter is 17 + 3x feet.
Answer:7x+12
Step-by-step explanation:
The 4 people in your crew each spent 4 hours laying sod. How many person-hours is this?
Since there are 4 people and they each spent 4 hours working, all we have to do is multiply the number of people (4) by the amount of hours each person spent (4)
4 x 4 = 16
Therefore, the total amount of hours is 16
Hope this helps you
-AaronWiseIsBae
Answer:
16 hours
Step-by-step explanation:
Given: There are 4 people in your crew.
Each spent 4 hours of laying sod.
To find the person hours, we have to multiply the number of people (4) by the amount of hours each person spent (4).
Total number of hours = Number of persons * Number of hours spent
Total number of hours = 4 x 4 = 16 hours
Therefore, the total amount of hours is 16.
7. A line in the Cartesian plane passes through the points (1, 3) and (5, 4). What is the slope of the line? A. 1/4 B. –4/1 C. 4/1 D. –1/4
A
to calculate the slope m , use the ' gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (5, 4)
m = [tex]\frac{4 - 3}{5 - 1}[/tex] = [tex]\frac{1}{4}[/tex] → A
What is the quotient of 59,584 divided 14
Answer:
4256
Step-by-step explanation: