Answers
9514 1404 393
Answer:
23) x = ±3i, ±√2
26) x = 4/3, (-2/3)(1 ± i√3)
Step-by-step explanation:
23) Put in standard form to make factoring easier.
x^4 +7x^2 -18 = 0
(x^2 +9)(x^2 -2) = 0 . . . . factors in integers
Using the factoring of the difference of squares, you can continue to get linear factors in complex and irrational numbers:
(x -3i)(x +3i)(x -√2)(x +√2) = 0
x = ±3i, ±√2
___
26) This will be the difference of cubes after you remove the common factor.
81x^3 -192 = 0
3(27x^3 -64) = 0
(3x -4)(9x^2 +12x +16) = 0 . . . . . factor the difference of cubes
The complex roots of the quadratic can be found using the quadratic formula.
x = (-12 ±√(12^2 -4(9)(16)))/(2(9)) = (-12 ±√-432)/18 = -2/3 ± √(-4/3)
Then the three solutions to the equation are ...
x = 4/3, (-2/3)(1 ± i√3)
Related Questions
Write down the next two terms in these quadratic sequences:
1.
9, 13, 19, 27,
2.
-5, 0, 9, 22,
Answers
and i’m not sure about the 2nd one
Given 2m+n=r, solve for m.
Answers
Answer:
m= r-n/2
Step-by-step explanation:
2m+n=r
2m=r-n
m=r-n/2
g(t) = (t 1)2 = 20.25
1) What are the zeros of the function?
Write the smaller t first, and the larger t second.
Answers
Answer:
The zeros are (-5.5, 0) and (3.5, 0).
Step-by-step explanation:
g(t) = (t + 1)² − 20.25
0 = (t + 1)² − 20.25
20.25 = (t + 1)²
±4.5 = t + 1
t = -1 ± 4.5
t = -5.5 or 3.5
Someone please help me with this
Answers
Answer:
The area of the shaded figure is:
20 units^2Step-by-step explanation:
To obtain the area of the shaded figure, first, you must calculate this as a rectangle, with the measurements: wide (4 units), and long (6 units):
Area of a rectangle = long * wideArea of a rectangle = 6 * 4Area of a rectangle = 24 units^2How the figure isn't a rectangle, you must subtract the triangle on the top, so, now we calculate the area of that triangle with measurements: wide (4 units), and height (2 units):
Area of a triangle = [tex]\frac{wide*height}{2}[/tex]Area of a triangle = [tex]\frac{4*2}{2}[/tex]Area of a triangle =[tex]\frac{8}{2}[/tex]Area of a triangle = 4 units^2In the end, you subtract the area of the triangle to the area of the rectangle, to obtain the area of the shaded figure:
Area of the shaded figure = Area of the rectangle - Area of the triangleArea of the shaded figure = 24 units^2 - 4 units^2Area of the shaded figure = 20 units^2I use the name "units" because the exercise doesn't say if they are feet, inches, or another, but you can replace this in case you need it.
Helppp +star & +15 points
Answers
Answer:
y=1
Step-by-step explanation:
the slope is 0 and the y-intercept is 1, so y=0x+1, y=1
Find the Error What error did the student make when solving the equation: 5x + 6 = 66 5x - 6 = 66 -6 5x = 60 5*5x= 60*5 X = 300 The student subtracted 6 from both sides instead of adding Student multiplied by 5 Vinstead of dividing by 5 Student got the wrong answer when subtracting 66-6 The student did not correctly eliminate the variable from one side of the equation
Answers
Answer:
The student multiplied by 5 instead of dividing by 5
Step-by-step explanation:
At the fourth step, the student multiplied each side by 5 rather than dividing it by 5. The opposite opperation from multiplication is division so they should have divided 5x and 60 by 5 here instead of multiplying it by 5. If this equation was done correctly, the correct answer would be x=12.
Show your work to evaluate g(f(x)) if f(x)=x+2/2 and g(x)=1x−1
Answers
Answer:
x/2.
Step-by-step explanation:
We replace the x in g(x) by f(x):
g(f(x)) = 1((x + 2/2) - 1
= (x + 2)/2 - 1
= (x + 2 - 2)/2
= x/2.
Answer:
x/2
Step-by-step explanation:
g(f(x)) = (x+2/2) - 1
= [tex]\frac{x+2}{2}[/tex] - [tex]\frac{2}{2}[/tex]
= (x + 2 - 2) / 2
= x/2
Solve the equation for all values of x by completing the square.
x² – 18x= -66
Answers
Answer:
x=12.87298334
Step-by-step explanation:
Simplify the expression below.
Answers
Answer:
[tex]\displaystyle 6[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{7^2 - 13}{24 - 18}[/tex]
Step 2: Evaluate
[Fraction] Exponents: [tex]\displaystyle \frac{49 - 13}{24 - 18}[/tex][Fraction] Subtract: [tex]\displaystyle \frac{36}{6}[/tex][Fraction] Divide: [tex]\displaystyle 6[/tex]Taylor is buying a chest freezer that had an original price of $145 but is
advertised at 25% off. Sales tax of 6.75% is applied to the discounted price.
How much will Taylor pay for the chest freezer?
a. $108.75 b. $116.09
C. $7.34
d. $108.08
Answers
Answer:B
Step-by-step explanation:
It's 116.09
Can someone explain how to do this I'm lost.
Answers
Step-by-step explanation:
[tex]\huge\bold\purple{ 5 }[/tex]
[tex]\huge\bold\purple{ explanation }[/tex]
[tex]90(right \: angle) = (9x + 1) + (7x + 9) \\ 90 = 16x + 10 \\ 16x = 90 - 10 = 80 \\ x = 80 \div 16 \\ x = 5| [/tex]
Is A ABC-A DEP? If so, identify the similarity postulate or theorem that
applies.
A. Similar - SAS
B. Similar - SSS
C. Similar - AA
D. Cannot be determined
Answers
Answer:
The similarity postulate that applies is;
C. Similar - AA
Step-by-step explanation:
The given parameters are;
ΔABC with angles ∠BAC = 30°, ∠ABC = 100° and ∠BCA = 50°
ΔDEF with angles ∠EDF = 30°, ∠DEF = 100° and ∠DFE = 50°
Therefore, the interior angles of ΔABC are equal to the corresponding interior angles of ΔDEF, which satisfies the Angle-Angle (AA) condition for similarity of two triangles based on the congruency of two interior angles of one triangle to two interior angles of the other triangle.
Please help!!:
1. Write the equation of a line that is perpendicular to y= -1/3 x+6 and passes through the point (3,5).
2. Write the equation of a line that is parallel to y = 2x – 4 and passes through the point (-3, 4).
Answers
-1/3*b=-1
b=3
5=3(3)+b
5=9+b
b=-4
equation of the line is y=3x-4
2) parallel lines have the same gradient
4=2(-3)+b
4=-6+b
b=10
equation of the line is y=2x-10
Help anyone? I need the questions worked out it doesn’t matter if you give me only one question
Answers
y2-y1/x2-x1. For A and B y2=4, y1=-4, x2=2 and x1=-2... Now u plug them in them, 4-(-4)/2-(-2)= 8/4=2. Slope equals 2. :)
In an electronics store, an iPod is $75. The sales tax is 7.5%. What is the cost of the iPod?
Answers
Answer:
$80.625
Step-by-step explanation:
$75 for the iPod times 0.075 = 5.625 which is the sales tax.
Then $75 (Cost of iPod) + 5.625 (Sales Tax) = $80.625 (Price of the iPod including the sales tax)
Sorry, if I am wrong. I tried my best and Hope this helps ;)
this is a personal question what do you do if your little sister will not stop bothering you and you are home allowen?
Answers
Answer: first try seeing what she wants and if that doesn’t work. either put on her favorite show with some snacks or go somewhere where you know she can’t find you. ☺️
Step-by-step explanation:
nancy is making cupcakes for her schools bake sale. after 2 hours of work she has 41 cupcakes after 7 hours she has 141 cupcakes. write an equation to model the number of cupcakes y for cupcakes x for hours
Answers
y = 20x + 1
John sales model boats from a booth at a local fair. He purchases each model boat from a distributor for five dollars and the local fair chargers him a baby and $80 John cells each model boat for $50. Write a system of equations to represent the situation
Answers
Answer and explanation:
Profit from sale of model boats = Sales -costs(costs of goods purchases + expenses or charges by the local fair)
John's profit from the sale of model boats can be represented by the equation:
P= 50x-(5x+80)
Where P is profit from the sale of the model boats and x is number of model boats bought and sold. The 80 is constant as it is a fixed cost paid to the local fair.
For example if John buys and sells 20 model boats, he would make profit of:
Substitute x=20 in equation above
P= 50×20-(5×20+80)
P=1000-180
P=$820
It could be said that John is in a very profitable business and his profit is also dependent on volume of sales because the lower his sales the closer he gets to making a loss and not profit
Help me with this too please hrlp
Answers
Answer:
3 * 10^4
Step-by-step explanation:
Here, we want to make a division
We want to divide 9 * 10^2 by 3 * 10^-2
That would be;
(9 * 10^2)/(3 * 10^-2)
= 9/3 * 10^2-(-2)
= 3 * 10^4
What are the solutions to the following system of equations? Select the correct answer below.
y = x2 - 4x + 3
2x + y = 6
A) (-1,8) and (3,0)
B) (-1, 3) and (8,0)
C) (0,8) and (3, -1)
D) (3, 8) and (-1,0)
Answers
Answer:
A
Step-by-step explanation:
we can conclude from the second equation that when
2x + y = 6 then y = 6 - 2x. so instead of y in the first equation we use 6 - 2x.
now the equation would look like this : 6 - 2x = x^2 - 4x + 3 .
then we bring everything to one side of the equation : x^2 - 2x - 3 .
now we'll have two results for x ( because x^2 - 2x - 3 = 0 has 2 answers )
one of them is -1 and other one is 3.
if we put them in the first equation we will have 8 and 0 for y.
so A is the answer
In a room of 200 people, 22% have blue eyes. How many people have blue eyes?
Answers
Answer: 44 people
Step-by-step explanation: 200 x .22=44
how do I simplify the expression -2.4+0.5f-14-4
Answers
9514 1404 393
Answer:
0.5f -20.4
Step-by-step explanation:
There is only one term containing a variable (0.5f), but there are three constant terms. The constant terms can be combined by finding their sum in the usual way.
-2.4 +0.5f -14 -4
= 0.5f -(2.4 +14 +4)
= 0.5f -20.4
Read the caption please, thank u so much!!!
Answers
Answer:
[tex]\huge\boxed{\sf S = 8}[/tex]
Step-by-step explanation:
Opposite sides and angles of a ║gm are equal.
So,
6S - 8 = 3S + 16
6S - 3S = 16 + 8
3S = 24
Divide 3 to both sides
S = 24 / 3
S = 8
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Carrie spent
1
4
of her allowance on a shirt,
1
3
of her allowance on a skirt, and $8 on a belt. If she spent $22 in all, how much was Carrie’s allowance?
Equation:
1
4
a +
1
3
a + 8 = 22
Carrie’s allowance was $.
Answers
Answer:
$24
Step-by-step explanation:
Let the total amount of her allowance = a
We are told that she spent $8 on belt
And the total amount she spent = $22
The Fraction of allowance spent on
Shirt = 1/4
Skirt = 1/3
Hence, the equation is given as:
1/4 × a + 1/3 × a + $8 = $22
Collect like terms
a/4 + a/3 = $22 - $8
a/4 + a/3 = $14
The Lowest Common Denominator = 12
3a + 4a/12 = $14
7a/12 = $14
Cross Multiply
7a = $14 × 12
7a = $168
a = $168/7
a = $24
Therefore, her total allowance = $24
Answer:
its 24 i took the quiz :)
Write an explicit formula for an, the nth term of the sequence 75, 15, 3, ....
Answers
Answer:
aₙ = 75 x 0.2ⁿ⁻¹ or 75 x (1/5)ⁿ⁻¹
Step-by-step explanation:
a₁ = 75
a₂ = 75 x 0.2¹ = 75 x 0.2 ²⁻¹ = 15
a₃ = 75 x 0.2² = 75 x 0.2³⁻¹ = 3
.......
aₙ = 75 x 0.2ⁿ⁻¹ or 75 x (1/5)ⁿ⁻¹
ack plots points showing equivalent ratios on the coordinate plane below.
m c 0 16- 1. g
Which ordered pair, if plotted above, would represent a ratio that is equivalent to those shown?
(1, 9)
(3, 9)
(4, 18)
Answers
Answer:
(4, 18)
Step-by-step explanation:
Our friend purchased a medium pizza for $10.31 with a 30% off coupon. What is the price of a medium pizza without a coupon? Do not include units (dollars) in your answer.
Answers
Answer:
the price of a medium pizza without a coupon is 14.73
Step-by-step explanation:
The computation of the price of a medium pizza without a coupon is given below:
Given that
The Price of medium pizza be 10.31 after considering the 30% off coupon
That means it is 70% value
So the 100% value would be
= 10.31 × 1 ÷ 0.70
= 14.73
hence, the price of a medium pizza without a coupon is 14.73
A chocolate bar is 3/4 of an inch long. If it is divided into pieces that are 3/8 of an inch long, then how many pieces is that?
Answers
Answer:
2 pieces
Step-by-step explanation:
3/4 = 6/8 (multiply by 2/2)
[tex]\frac{6}{8}/\frac{3}{8} =\frac{6}{8} * \frac{8}{3} = \frac{6}{3} =2pieces[/tex]
Gerri is working on a project that need to be finish by Friday so far she has completed 1/3 of the project How much of the project does she have to finish By Friday . Answer is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Answers
Answer:
Part of incomplete work = 2/3 of project
Step-by-step explanation:
Given:
Part of work completed = 1/3 of project
Find:
Part of incomplete work
Computation:
Part of incomplete work = 1 - Part of work completed
Part of incomplete work = 1 - 1/3
Part of incomplete work = 2/3 of project
what is the equation that passes through the given point and has the given slope (-2, -1); m= -3
Answers
Answer:
y = - 3x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 3, then
y = - 3x + c ← is the partial equation
To find c substitute (- 2, - 1) into the partial equation
- 1 = 6 + c ⇒ c = - 1 - 6 = - 7
y = - 3x - 7 ← equation of line
Answer:
The equation would be y=-3x-7
Step-by-step explanation: