Answer:
f(x)=(x+2)(x−(−1+i2√))(x−(−1−i2√))
Sorry if its wrong!
The required completely factored form is f(x) = (x + 2)(x−(−1+i2√))(x−(−1−i2√)).
What is the Factorization?Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).
The function is given in the question following as:
f(x) = x³ + 4x² + 7x + 6
We have to determine the completely factored form of the given function
As per the given question, we have
⇒ f(x) = x³ + 4x² + 7x + 6
Common factor as (x + 2) out in the above expression,
⇒ f(x) = (x + 2)(x² + 2x + 3)
⇒ f(x) = (x + 2)(x−(−1+i√2))(x−(−1−i√2))
Therefore, the required completely factored form is f(x) = (x + 2)(x−(−1+i2√))(x−(−1−i2√)).
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Question 4
Two spinners are spun +
and the scores are added
together. The results are
shown in the diagram
opposite.
2
a) Write down the
probability that the || 3
score is 3
b) Write down the
probability that the
score is an even
number.
c) If the two spinners
are spun 200 times,
how many times
would you expect
the score to be 2.
Answer:
a is 7/25
b is 14/25
c is 24
Step-by-step explanation:
a) because there are 25 possible outcomes and 7 of them are 3 it is 7/25
b) using the same logic 14 possible outcomes are even
c) because the probability of it being 2 is 3/25, which can be made into ?/200 by multiplying the 25 by 8, which means we have to do the same to the 3, making it 24
Amber got a raise, and her hourly wage increased from $8 to $9.50 what is the percent increase
Answer:
The percent increase is 18.75%.
Step-by-step explanation:
Given:
Amber got a raise, and her hourly wage increased from $8 to $9.50.
Now, to find percent increase.
Previous wage = $8.
Wage raised = $9.50.
So, to get the increased wage we subtract the previous wage from the wage raised:
[tex]\$9.50-\$8=\$1.50.[/tex]
Now, to get the percent increase:
[tex]\frac{1.50}{8} \times 100[/tex]
[tex]=\frac{150}{8}[/tex]
[tex]=18.75\%.[/tex]
Therefore, the percent increase is 18.75%.
The percent increase in Amber's hourly wage from $8 to $9.50 is 18.75%.
To find the percent increase in Amber's hourly wage, you can follow these steps:
Find the difference between the new wage and the old wage:⇒ $9.50 - $8 = $1.50.
Divide the difference by the old wage to find the percentage change:⇒ $1.50 ÷ $8 = 0.1875.
Convert the decimal to a percentage by multiplying by 100:⇒ 0.1875 × 100 = 18.75%.
Therefore, the percent increase in Amber's hourly wage is 18.75%.
Complete question:
Amber got a raise and her hourly wage increased from $8 to $9.50. What is the percent increase?
What is the product of the 6th square number and the 5th square number?
The solution is 900
The product of the 6th square number and 5th square number is given by the equation A = 900
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be a
The value of a = 6th square number
a = 6²
The value of a = 36
Let the second number be b
The value of b = 5th square number
a = 5²
The value of b = 25
Now , the equation is
A = first number x second number
Substituting the values in the equation , we get
A = 25 x 36
A = 900
Therefore , the value of A is 900
Hence , the equation is A = 900
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Final answer:
The product of the 6th square number (36) and the 5th square number (25) is 900.
Explanation:
To find the product of the 6th square number and the 5th square number, we first need to identify what those square numbers are.
A square number is a number multiplied by itself.
The 6th square number is 6², which is 36.
The 5th square number is 5², which is 25.
Now, to find the product, we multiply these two square numbers together:
36 × 25 = 900
Therefore, the product of the 6th square number (36) and the 5th square number (25) is 900.
A cereal mixture contains Almond, Wheat, and Corn in the ratio of 3:5:7. What amount of this mixture contains 9 kilograms of Almond?
The total cereal mixture is 45 kilograms
Solution:
Given that, cereal mixture contains Almond, Wheat, and Corn in the ratio of 3:5:7
Therefore,
Almond : Wheat : Corn = 3 : 5 : 7
Let the almond present be 3x
Let the wheat present be 5x
Let the corn present be 7x
Therefore,
Total cereal mixture = 3x + 5x + 7x
Total cereal mixture = 15x
Given that mixture contains 9 kg of almond
Almond = 9
We know that,
Almond present = 3x
3x = 9
x = 3
Therefore,
Total cereal mixture = 15x = 15(3) = 45
Thus total cereal mixture is 45 kilograms
#14 Lia spend $4 more on
her backpack than Kiera.
Write an algebraic
expression that represents
the situation.
Answer:
x=y+4
Step-by-step explanation:
Amount spent by Lia=x
Amount spent by Kiera=y
x=y+4
Answer: [tex]k+4[/tex]
Step-by-step explanation:
You need to analize the data given in order to solve the exercise.
First, it is important to remember that, in Word problems the word "more" indicates Addition.
In this case, let "k" represents the amount of money (in dollars) that Kiera spends on her backyard.
Accordding to the information provided in the exercise, you know that Lia spends $4 dollars more on her backyard than Kiera spends on her backyard.
Therefore, you can identify that the amount of money that Lia spends can be found by adding the amount of money Kiera spends and $4.
Based on the above, you can determine that this situation can be represented with the following expression:
[tex]k+4[/tex]
Triangle X Y Z is shown. Angle Y X Z is a right angle. The length of Y X is 12 inches and the length of X Z is 10 inches. Angle X Y Z is x. Which is the best approximation for the measure of angle XYZ? 33.6° 39.8° 50.2° 56.4°
The best approximation for the measure of angle XYZ is 39.8° ⇒ 2nd answer
Step-by-step explanation:
Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle
The trigonometry ratios of the angle BAC, the opposite side to this angle is BC and the adjacent side to it is AB are
[tex]sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}[/tex] [tex]cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}[/tex] [tex]tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}[/tex]In Δ XYZ
∵ ∠ YXZ is a right angle
∴ The hypotenuse is YZ
∵ The adjacent side to ∠XYZ is XY
∵ The opposite side to ∠XYZ is XZ
∵ YX = 12 units
∵ XZ = 10 units
- Use tan ratio to find the measure of the angle because you
have the adjacent and opposite sides of the angle XYZ
∵ m∠XYZ is x
∵ [tex]tan(x)=\frac{XZ}{XY}[/tex]
∴ [tex]tan(x)=\frac{10}{12}[/tex]
- To find x use the inverse of tan(x)
∵ [tex]x=tan^{-1}(\frac{10}{12})[/tex]
∴ x = 39.8°
∴ m∠XYZ = 39.81°
The best approximation for the measure of angle XYZ is 39.8°
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Answer:
B 39.8
Step-by-step explanation:
just took the test!
One gallon of paint usually covers about 350 square feet. How many square feet will 2.5 gallons cover? Show your
work, including labeling your answer with the appropriate units of measure.
Answer:875 feet
350÷2=175
350+350+175=875
Step-by-step explanation:
Eva was playing a game with a friend and had 100 points.
Then, she drew a bad card and lost 120 points.
What was her new score?
She had 100 points then lost 12-0 points.
Subtract 120 from 100.
100 - 120 = -20
Answer:20
Step-by-step explanation:
Factor the expression completely.8y - 36
A 4(2y - 9)
B 8(y – 4)
C -4(2y + 9)
D 2(4y - 18)
Answer:
A. 4(2y-9)
Step-by-step explanation:
Both terms are divisable by 4 and would bring them to the smallest whole degree
Answer:
your answer will be D.
Step-by-step explanation:
2x4y= 8y
2x (-18)= -36
Find the common difference for the given sequence. Type a numerical answer in the space provided. Do not include
spaces in your answer. If necessary, use the key to represent a fraction bar
105, 110, 115, 120.
Answer: -5
Step-by-step explanation:
Answer: 5
Step-by-step explanation:
The formula for calculating common difference is given by :
[tex]t_{2}[/tex] - [tex]t_{1}[/tex] = [tex]t_{3}[/tex] - [tex]t_{2}[/tex] = [tex]t_{4}[/tex] - [tex]t_{3}[/tex]
Where [tex]t_{1},t_{2}[/tex] are the terms given .
from the sequence given :
[tex]t_{1}[/tex] = 105
[tex]t_{2}[/tex] = 110
[tex]t_{3}[/tex] = 115
[tex]t_{4}[/tex] = 120
Therefore : common difference will be
110 - 105 = 5
115 - 110 = 5
120 - 115 = 5
Therefore , 5 is the common difference
- 1\2[p+2]= -3 -p
Can somebody solve this for me ! plz
Answer:
-4
Step-by-step explanation:
-1(p+2)/2=-3-p
Multiplying both sides by 2
-p-2=2(-3-p)
-p-2=-6-2p
Combining similar terms
-p+2p=-6+2
p=-4
A sky jump makes an angle of 27° with respect to the water as shown below. How are the 27° angle and the unknown angle related? What is the value of X?
Answer:
153
Step-by-step explanation:
The figure shows a right triangle with acute angle of 27°, this angle is the angle between the water level and the ski ramp.
It is also shown the suplementary angle 27° marked as X°, which is the angle that you must determine.
In the figure is clear that x is the exterior angle of the corner with the angle of 27° and that X° + 27° = 180°.
Then you can solve for X.
X = 180° - 27° = 153°.
Answer: 153°
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-(2)negative negative two quotation to the zero power equals
Answer:
1
Step-by-step explanation:
While I am not 100% sure what you are putting (I'm assuming it's -2^0), anything to the power of 0 will equal a positive 1 as your answer.
What are the next two terms in the pattern 3,6,5,,10,9,18,17
Answer:
34,33
Step-by-step explanation:
3×2=6
6-1=5
the pattern is multiplied by 2 minus1
I NEED THE ANSWER ASAP PLEASE
Answer:
720$
Step-by-step explanation:
(1000+(230*24))-5800=720
What is the radius of a circle with the equation x2 + y2 – 14x + 10y = 250?
Answer:
18
Step-by-step explanation:
x^2 + y^2 – 14x + 10y = 250
x^2 -14x + y^2 + 10y = 250
x^2 - 14x + (-7)^2 + y^2 + 10y + (5)^2 = 250 + (-7)^2 + (5)^2
(x-7)^2 + (y + 5)^2 = 250 + 49 + 25
(x-7)^2 + (y + 5)^2 = 324
Comparing with the general circle (x - b)^2 + (y - a)^2 = r^2
we have; r^2 = 324
r = square root(324)
r = 18
The equation A = x(x-4) describes the area, A, of a rectangular flower garden, where x is the width in feet.
What would be the width in feet of the flower garden if the area is 12 square feet?
A.2
B.6
C.4
D.7
Answer:
The flower garden width would be 6 ft
Step-by-step explanation:
A = 12 ft^2 = x(x + 4) becomes:
x^2 + 4x - 12 = 0, or (by completing the square) x^2 + 4x + 4 - 4 - 12 = 0
Thus, we have (x + 2)^2 - 16 = 0, or (x + 2)^2 = 16
Taking the square root of both sides yields x + 2 = ±4.
In this context only a positive x value makes sense: x = 2 + 4 => x = 6.
The flower garden width would be 6 ft. The other dimension would be 6 - 4, or 2, ft.
To find the width of the flower garden when the area is 12 square feet, the equation A = x(x-4) is used. Solving for x, the width of the flower garden is 6 feet.
To find the width of the flower garden when the area is 12 square feet:
Plug in A=12 into the equation: 12 = x(x-4)
Solve the equation for x by factoring or using the quadratic formula
The possible values for x are 6 and -2, but since width can't be negative, the width of the flower garden is 6 feet (B)
Wang Xiu Ying has
109
109109 dollars in her savings account. She has
−
21
−21minus, 21 dollars in her checking account.
Write an inequality that correctly compares the account values.
Which one of the following descriptions is correct?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Wang Xiu Ying's checking account has a lower account value than her savings account.
(Choice B)
B
Wang Xiu Ying's savings account has a lower account value than her checking account.
Answer:
109>21
Answer is A.
Step-by-step explanation:
When we read this example. We can conclude :
Saving account : $109
Checking : $21
So:
Wang Xiu Ying's checking account has a lower account value than her savings account.
Answer: 109>-21
B
Step-by-step explanation:
Delia is hosting a BBQ. She buys a total of 50 burgers and Hot Dogs for $90. Delia pays $2 per burger and $1.50 per Hot Dog. Write a system of linear equations to find the number x of burgers and the number y of Hot Dogs Delia buys. Solve the linear system by substitution. Please help-
z=a/b+c/d solve for D
Final answer:
To solve for D in the equation z = a/b + c/d, subtract a/b from both sides, combine fractions on the left side, cross multiply, and finally solve for d by dividing both sides by (bz - a).
Explanation:
To solve for D in the equation z = a/b + c/d, you need to isolate d on one side of the equation. Here's how you can do it:
Subtract a/b from both sides of the equation: z - a/b = c/d.Find the common denominator for the left side of the equation, then combine fractions: (bz - a)/b = c/d.Cross multiply to get rid of the fractions: d(bz - a) = bc.Divide both sides by (bz - a) to solve for d: d = bc/(bz - a).When a = 2.658653234, b = 0.179825026, c = -54.56945917, and z = 17.98260265, you would substitute these values and calculate d accordingly, leading to a numerical solution for d.
Find the perimeter of a rectangle whose dimensions are 15 inch times 8 inches
A rectangular piece of metal is 25 in longer than it is wide. Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2730 in^3, what were the original dimensions of the piece of metal?
Answer:24 oringal width
49 original length
Step-by-step explanation:
The original dimensions of the rectangular piece of metal were 30 inches by 55 inches, based on the given conditions of making an open box and its volume.
Explanation:In this problem, we have a rectangular piece of metal that is being converted into an open box. Note that the length of the rectangular piece is 25 in longer than its width.
When squares with side 5 in are cut from the corners and the sides are folded up to make the open box, the dimensions of the box formed become length = w+25-10, width = w-10, and height = 5, where w is the width of the original rectangular piece.
The volume of a box is given by the product of length, width, and height. So if the volume of this box is given as 2730 cubic inches, we can write the equation (w-10)(w+15)(5)=2730.
This can be solved to give w=30 (excluding the negative solution as unrealistic for this context). Therefore, the original dimensions of the metal piece were 30 in (width) by 55 in (length).
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The director of a production company constructed the Venn diagram shown to display the types of employees in the company. How many of the employees are both actors and dancers?
Answer:
9
Step-by-step explanation:
The way to find the answer is by finding the point we're the two circles intersect and adding the number in that space to the number in the middle as the people in the middle are shown to be capable of both things as well
Is 120 of 100 larger than 100
Answer:
No
Step-by-step explanation:
120/100 is the same as 1 20/100 or 1 2/10. 1 2/10 is not greater than 100
Answer:
Step-by-step explanation:
nop
A new notebook computer with DVD player cost $808 Derek muller has $969 in his checking account how much will be left in his checking account after he buys the notebook computer
Answer: $161
Step-by-step explanation: Subtract $808 from $969
Answer: he will have $161 in his account after he buys the computer and dvd player.
Step-by-step explanation:
First, do 969-808 and you simply get 161 as your answer
So, for this problem you are simply subtracting
* brainliest answer this plz....
Which algebraic expression is represented by the model?
A. 3 ( 3 x + 9 ) B. 3 x ( x + 3 ) C. 3 ( x + 3 ) D. 3 ( x + 9 )
Answer:
Contributing
Step-by-step explanation:
Just contribute the number that is not is the column to the number that is in the column
Final answer:
The provided expressions each represent different algebraic operations. The first involves rearranging a quadratic equation into standard form, while the second describes the line and graph representation of a linear equation. The third is the application of the product rule to find the derivative of an equation.
Explanation:
To determine which algebraic expression is represented by the model, the given expression of 3x +3+x²+x=24 needs to be simplified and put into standard form. This involves combining like terms and rearranging to achieve the form ax² +bx+c= 0. After combining terms involving x and rearranging, you should subtract 24 from both sides of the equation to set it equal to zero.
On the other hand, the equation y = 9 + 3x represents a linear relationship with a slope (m) of 3 and a y-intercept (b) of 9. Constructing a table or graph of this equation by plugging in different x-values and calculating y reveals a line on a graph. The given equation has no terms that would suggest it represents a model that includes x², thus it is not a quadratic equation and does not match the first expression.
When dealing with the derivative of the equation (x³)'(1 + x²)−¹ + x³ [(1 + x²)−¹]', according to the product rule, this simplifies to 3x² (1 + x²)−¹ + x³ [-(1 + x²)−²(2x)]. Simplifying further, you obtain a final form that involves squaring the binomial (1+x²).
These three examples of algebraic manipulation showcase different types of operations needed to simplify and derive equations for specific purposes.
A wire 18 ft long is cut into two pieces. Each piece is bent into the shape of a square. The perimeter of the larger square is twice the perimeter of the smaller square. Find the perimeter of the larger square.
Answer:
12
Step-by-step explanation:
18/3=6
If one piece is twice as large as the other, than 18 needs to be divided by 3, making it exact.
Answer:12
Step-by-step explanation:
Perimeter of a square =4L
Perimeter of larger square is twice the perimeter of square =2x4L=8L
Wire length =18ft
Wire length =sum of the two perimeterr
18=4L+8L
18=12L
L=18/12
L=1.5
Perimeter of larger square=8L
Replace Lwith 5
Perimeter of larger square =8x1.5
Perimeter of larger square =12ft
Help me please I really don’t get this
Answer:
y equals 45, because you substitute the x in the bigger equation with -2, and then solve for y
How does adding or subtracting polynomials compare to adding or subtracting integers?
Answer:
Subtracting Polynomials is very similar to adding polynomials. In fact, we will be changing the subtraction problem to an addition problem. In the Pre-Algebra section of the website, we started out by reviewing integers. We said, " When you subtract integers, you must add the opposite. We also talked about the Keep - Change- Change Rule.
Step-by-step explanation:
The explanation regarding the adding or subtracting polynomials compare to adding or subtracting integers is explained below:
The following information should be considered:
Subtracting Polynomials is same to adding polynomials. It should be changed the subtraction problem to an addition problem. In the Pre-Algebra section of the website, here we begins with reviewing integers. We said that at the time when you subtract integers, you must add the opposite. Also, Keep - Change- Change Rule should be considered.
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Holly spilled 1/4 of her 2-liter bottle of soda How much soda does she have left?
Answer:
3/4
Step-by-step explanation:
im a big brain so yea