The solutions of the polynomial are [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
Step-by-step explanation:
The solutions of a polynomial is the value of x when the polynomial equal to zero
The formula of quadratic polynomial is [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}[/tex] , where
a is the coefficient of x²b is the coefficient of xc is the numerical term∵ The polynomial is 4x² - 4x + 10
- Equate it by zero to find its solutions
∴ 4x² - 4x + 10 = 0
∵ The coefficient of x² is 4
∴ a = 4
∵ The coefficient of x is -4
∴ b = -4
∵ The numerical term is 10
∴ c = 10
- Use the formula to find the values of x
∵ [tex]x=\frac{(-4)(+/-)\sqrt{(-4)^{2}-4(4)(10)}}{2(4)}[/tex]
∴ [tex]x=\frac{-4(+/-)\sqrt{16-160}}{8}[/tex]
∴ [tex]x=\frac{-4(+/-)\sqrt{-144}}{8}[/tex]
∵ [tex]\sqrt{-144}=12\sqrt{-1}[/tex]
- Substitute [tex]\sqrt{-1}[/tex] by i
∴ [tex]12\sqrt{-1}=12i[/tex]
∴ [tex]x=\frac{-4(+/-)12i}{8}[/tex]
- Divide up and down by 4 to simplify the fraction
∴ [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
The solutions of the polynomial are [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
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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
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
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.
does 490/10 equel to 4.9
Answer:
No it equals to 49
Step-by-step explanation:
490÷10=49
Seven tenths minus one half
Answer:
7/10 - 1/2 = 7/10 - 5/10 = 2/10 = 1/5 (one fifth)
Step-by-step explanation:
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....
Set up a percent ratio to help find the part given the percent and the whole. On a 50-point quiz, Jenna earned 82% of the points. How many points did she earn?
Joe is going to rent a truck for one day.company A has no initial fee but charges 80 cents for every mile driven. Company B charges an initial fee of $50 and an additional 60 cents for every mile driven.for what mileage will company A charge more than company B?
Answer:
Therefore the minimum mileage for which Company A will charge more than Company B is 251 miles.
Step-by-step explanation:
i) let x be the number of miles driven
ii) If Joe rents the truck from Company A the Joe will pay Company A
= $0.8x
iii) If Joe rents the truck from Company B then Joe will pay Company B
= $50 + $0.6x
iv) the mileage for which the rents of both companies will be equal is given by
$0.8x = $50 + 0.6x
Therefore 0.2x = $50
Therefore x = [tex]\frac{50}{0.2} = \frac{500}{2} = 250[/tex] miles.
Therefore the minimum mileage for which Company A will charge more than Company B is 251 miles.
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
Factor the following trinomials:
a) x^2 -2x -1
b) x^2 -3x+1
Final answer:
To factor the trinomials x^2 - 2x - 1 and x^2 - 3x + 1, you can use the quadratic formula or factoring by grouping.
Explanation:
To factor the trinomials x^2 - 2x - 1 and x^2 - 3x + 1, we can use the quadratic formula or factoring by grouping.
a) For x^2 - 2x - 1, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac))/(2a)
Plugging in the values, we have:
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-1)))/(2(1))
x = (2 ± sqrt(4 + 4))/(2)
x = (2 ± sqrt(8))/(2)
x = (2 ± 2sqrt(2))/(2)
x = 1 ± sqrt(2)
Therefore, the factored form is: x^2 - 2x - 1 = (x - (1 + sqrt(2)))(x - (1 - sqrt(2)))
b) For x^2 - 3x + 1, we can also use the quadratic formula:
x = (3 ± sqrt(3^2 - 4(1)(1)))/(2(1))
x = (3 ± sqrt(5))/(2)
Therefore, the factored form is: x^2 - 3x + 1 = (x - (3 + sqrt(5))/(2))(x - (3 - sqrt(5))/(2))
a) x^2 - 2x - 1 = (x - 1)(x + 1)
b) x^2 - 3x + 1 = (x - 1)^2
a) x^2 - 2x - 1:
This trinomial is in the form ax^2 + bx + c. To factor it, we need to find two numbers that:
Multiply to ac (in this case, 1 * -1 = -1).
Add up to b (in this case, -2).
These two numbers are -1 and 1.
So, we can rewrite the trinomial as:
(x - 1)(x + 1)
Therefore, the factored form of x^2 - 2x - 1 is (x - 1)(x + 1).
b) x^2 - 3x + 1:
This trinomial is also in the form ax^2 + bx + c. To factor it, we need to find two numbers that:
Multiply to ac (in this case, 1 * 1 = 1).
Add up to b (in this case, -3).
These two numbers are -1 and -1.
So, we can rewrite the trinomial as:
(x - 1)(x - 1)
However, it is common practice to simplify repeated factors, so the fully factored form of x^2 - 3x + 1 is (x - 1)^2.
Find 6 times as many as,2plus 9
Answer:
The answer is 21.
Step-by-step explanation:
6 * 2 = 12 + 9 = 21
Answer:
66
Step-by-step explanation:
The equation would go like this:
6(2+9)
Next you solve for parenthesis:
6(11)
Lastly multiply:
6(11)=66
4/9 is it equivalent to 20/36
Answer: No
Step-by-step explanation: In order to decide whether the given fractions are equivalent, first write each fraction in lowest terms.
A fraction is written in lowest terms if the greatest common factor of the numerator and the denominator is 1.
So for our first fraction, 4/9, since the greatest common factor of 4 and 9 is 1, we know that are fraction is already written in lowest terms.
For our second fraction however, since the greatest common factor of 20 and 36 is 4, we must divide both the numerator and the denominator by 4 to write our fraction in lowest terms. This gives us 5/9.
Since 5/9 is bigger than 4/9, te fractions are not equivalent so no, 4/9 is not equivalent to 20/36.
Your phones service plan costs $10 per month and .15 cents per minute to make a call. Write an equation that represents the cost to use your phone per month
Answer:
an equation for how much your phone costs per month=
.15x+10
What are the values of a, and r of the geometric series?
2-2+2-2+2
a = 2 and r=-2
a = -2 and r = 2
aq=-1 and r = 2
az = 2 and r=-1
Answer:
a = 2; r = -1
Step-by-step explanation:
a is the first term: 2
r is the ratio of successive terms: -2/2 = 2/-2 = -1.
Answer:
a = 2; r = -1
Step-by-step explanation:
a is the first term: 2
r is the ratio of successive terms: -2/2 = 2/-2 = -1.
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 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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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:
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!
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
Montell gets $10.50 each week for doing yard work for his neighbors. He has earned $63 so far. Write and solve an equation to find how many weeks it took for him to earn that amounts.
Answer:
10.50x = 63
You'll divide 63 by 10.50 to get 6 weeks.
If the entries of A + B are represented by Xij and the entries of A − B are represented by yij the value represented by x24 is and the value represented by y13 is .
Answer:
[tex]x_{24} = a_{2} +b_{4} \\y_{13} = a_{1} - b_{3}[/tex]
:)
Answer:
it -3 and 7
Step-by-step explanation:
A campus apartment has two bedrooms and two attached bathrooms and rents for $1,025 per month plus an average of $60 per month for electricity. You are a student and would have the option of splitting the rent with a fellow student 60/40. You pay 40% as your name is on the lease. Your scholarship gives you $700 per month for housing. What can you save above your out of pocket housing cost with your scholarship and your roommate's contribution in an Academic Year (8 months).
I can save $2,128 in my academic year and my roommate can save $392 in their academic year.
Step-by-step explanation:
Total housing amount= rent + electricity= $1,025 + $60= $1,085 per month
My rent is 40% of $1,085 which equals $434 a month while my roommate’s rent would be 60% of $1,085 which equals $651 a month.
The scholarship gives me $700 a month for housing out of which I spend $434 and my roommate spends $651.
I save; $700 - $434 = $266 a month
My roommate saves; $700 - $651 = $49 a month.
An academic year lasts for 8 months so my savings= $266 x 8 = $2,128
My roommate’s savings= $49 x 8 = $392
Answer:
$2,128
Step-by-step explanation:
Expenses is allocated based on the decided ratios. Expenses and Inflows
Expenses will be calculated for 8 Months time period.
Rent = 1,025 x 8 months = $8,200
Electricity Expense = $60 x 8 = $480
Total Expense = $8,200 + $480 = $8,680
Total Scholarship = $700 x 8 = $5,600
Out of Pocket Cost = $8,680 x 40% = $3,472
Saving is the difference between The scholarship received and the Expenses made from pocket.
Saving = $5,600 - $3,472 = $2,128
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
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.
#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]
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?
for what value of x is the rational expression below undefined? x-4 / 4+x a. 0 b. -4 c. -1 d. 4
Answer:
The answer is option b. -4
Step-by-step explanation:
Given: [tex]\frac{x-4}{4+x}[/tex]
the rational expression will be undefined at the zeros of the denominator
To find the zeros of the denominator
the denominator = 0
∴ 4 + x = 0
∴ x = -4
So, the rational expression will be undefined at x = -4
The answer is option b. -4
Answer:
b)
Step-by-step explanation:
[tex]\frac{x-4}{4+x}\ and\ 4+x\neq 0\ (we\ can't\ divide\ by\ 0)[/tex]
[tex]4+x\neq 0\\x\neq -4[/tex]
Find the sum: 2 1/3+1 3/4
Answer:
2 1/3 + 1 3/4
Step-by-step explanation:
First, find a common denominator which is 12.
2 4/12 + 1 9/12
= 4 1/12 or 37/12
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
-(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.