2a^3 + a^2 + a + 4
A Linear
B Cubic
C Quadratic
D: Quartic
Answer:
C. Quadratic
Step-by-step explanation:
Solve for a:
2 a^3 + a^2 + a + 4 = 0
Hint: | Look for a simple substitution that eliminates the quadratic term of 2 a^3 + a^2 + a + 4.
Eliminate the quadratic term by substituting x = a + 1/6:
23/6 + (x - 1/6)^2 + 2 (x - 1/6)^3 + x = 0
Hint: | Write the cubic polynomial on the left-hand side in standard form.
Expand out terms of the left hand side:
2 x^3 + (5 x)/6 + 104/27 = 0
Hint: | Write the cubic equation in standard form.
Divide both sides by 2:
x^3 + (5 x)/12 + 52/27 = 0
Hint: | Perform the substitution x = y + λ/y.
Change coordinates by substituting x = y + λ/y, where λ is a constant value that will be determined later:
52/27 + 5/12 (y + λ/y) + (y + λ/y)^3 = 0
Hint: | Transform the rational equation into a polynomial equation.
Multiply both sides by y^3 and collect in terms of y:
y^6 + y^4 (3 λ + 5/12) + (52 y^3)/27 + y^2 (3 λ^2 + (5 λ)/12) + λ^3 = 0
Hint: | Find an appropriate value for λ in order to make the coefficients of y^2 and y^4 both zero.
Substitute λ = -5/36 and then z = y^3, yielding a quadratic equation in the variable z:
z^2 + (52 z)/27 - 125/46656 = 0
Hint: | Solve for z.
Find the positive solution to the quadratic equation:
z = 1/216 (3 sqrt(4821) - 208)
Hint: | Perform back substitution on z = 1/216 (3 sqrt(4821) - 208).
Substitute back for z = y^3:
y^3 = 1/216 (3 sqrt(4821) - 208)
Hint: | Take the cube root of both sides.
Taking cube roots gives 1/6 (3 sqrt(4821) - 208)^(1/3) times the third roots of unity:
y = 1/6 (3 sqrt(4821) - 208)^(1/3) or y = -1/6 (208 - 3 sqrt(4821))^(1/3) or y = 1/6 (-1)^(2/3) (3 sqrt(4821) - 208)^(1/3)
Hint: | Perform back substitution with x = y - 5/(36 y).
Substitute each value of y into x = y - 5/(36 y):
x = 1/6 (3 sqrt(4821) - 208)^(1/3) - 5/(6 (3 sqrt(4821) - 208)^(1/3)) or x = -1/6 (208 - 3 sqrt(4821))^(1/3) - (5 (-1)^(2/3))/(6 (3 sqrt(4821) - 208)^(1/3)) or x = 5/6 ((-1)/(3 sqrt(4821) - 208))^(1/3) + 1/6 (-1)^(2/3) (3 sqrt(4821) - 208)^(1/3)
Hint: | Simplify each solution.
Bring each solution to a common denominator and simplify:
x = ((3 sqrt(4821) - 208)^(2/3) - 5)/(6 (3 sqrt(4821) - 208)^(1/3)) or x = -1/6 (208 - 3 sqrt(4821))^(1/3) - (5 (-1)^(2/3))/(6 (3 sqrt(4821) - 208)^(1/3)) or x = 1/6 (5 ((-1)/(3 sqrt(4821) - 208))^(1/3) + (-1)^(2/3) (3 sqrt(4821) - 208)^(1/3))
Hint: | Perform back substitution on the three roots.
Substitute back for a = x - 1/6:
Answer: a = ((3 sqrt(4821) - 208)^(2/3) - 5)/(6 (3 sqrt(4821) - 208)^(1/3)) - 1/6 or a = -1/6 - 1/6 (208 - 3 sqrt(4821))^(1/3) - (5 (-1)^(2/3))/(6 (3 sqrt(4821) - 208)^(1/3)) or a = 1/6 (5 (-1/(3 sqrt(4821) - 208))^(1/3) + (-1)^(2/3) (3 sqrt(4821) - 208)^(1/3)) - 1/6
solve the following equation c/4 = 4
Solve the literal equation 4a-2b=8b-5a
Answer:
if your solving for a its a=10b/9
Step-by-step explanation:
And electronics store chain sells headphones The company is about to introduce a new headphones model that is expected to sell very well across its various stores. The projected revenue and cost functions for the headphones are R(x)=-0.25x+25x and c(x)= -17+90. What is the profit function
Answer:
[tex]P(x) = -0.25x^2 + 42x - 90[/tex]
Step-by-step explanation:
Given
[tex]C(x) = -17x + 90[/tex]
[tex]R(x) =- 0.25x^2 + 25x[/tex]
Required
Determine the profit function.
Profit function is calculated as thus:
[tex]P(x) = R(x) - C(x)[/tex]
So, we have:
[tex]P(x) = -0.25x^2 + 25x -(-17x + 90)[/tex]
[tex]P(x) = -0.25x^2 + 25x + 17x - 90[/tex]
[tex]P(x) = -0.25x^2 + 42x - 90[/tex]
HELPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
C THERE YOU GO HERLRLP[PPPPPPP
Can someone help me Find F(2)
Answer: F(2)=23
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
f(x)= 4(2)^2 +7
f(x)= 4(4) +7
f(x)= 16+7
f(x) = 23
which equations have exactly one y-value for any given x-value? select all that apply
A.y=-x
B.x=4
C.y=x^2
D.y=x^3
Answer:x=4
Step-by-step explanation:
The equations y = -x,y = x², and y = x³ have one y-values for a given x-value thus options (A) ,(C) and (D) will be correct.
What is the equation?There are many different ways to define an equation.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
In the first option y = -x
The value of y will be negative of x thus it will be single for every single x.
In the third option x = x² here for every x there will be a single y thus it will be single for every single x.
In option fourth option y = x³ here for x, y will be one thus it will be single for every single x.
In option (B) x = 4 here y is changing for x = 4 thus here y will not be one.
Hence "The equations y = -x,y = x², and y = x³ have one y-values for a given x-value".
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A lumber company has 40,000
boards in stock. A construction
company bought 500 boards for
each of its construction projects. If
the lumber company has 12,000
boards left, how many construction
projects did the company have?
Answer:
12500
Step-by-step explanation:
we all know this is not high school math -_-
At midnight, the temperature was 20.4°F. In the morning, the temperature was −5.2°F. Which statement describes the temperatures?
Please help will give brainliest
Answer:
Hey dabi, the statment that describes the tempertures is one is cold the other is colder i guess
Step-by-step explanation:
if you know the answer you have a high IQ ->
Mrs. O’Connor is creating a large square painting with the grade 8 art classes. The painting will be made of 24cm by 32cm rectangles covered with colored squares. They want these squares to be as large as possible, measured in whole numbers of centimeters.
Then they plan to arrange copies of the 24cm by 32cm rectangle to form a large square painting that measures the least possible whole number of centimeters.
What size will the small colored squares be?
How big will the painting be?
9514 1404 393
Answer:
small squares: 8 cm squarelarge painting: 96 cm squareStep-by-step explanation:
The size of the small squares will be the greatest common divisor (GCD) of the dimensions 24 cm and 32 cm. We know these dimensions can be factored as ...
24 = 3×8
32 = 4×8
so the GCD is 8 cm.
The rectangles can be covered with squares that are 8 cm on a side.
__
The dimensions of the painting will be the least common multiple of the rectangle dimensions. That is ...
LCM(24, 32) = 24×32/GCD(24, 32) = 24×32/8 = 96
The smallest square painting that can be made from these rectangles is 96 cm square.
Simplify the following expression
- 4p - (1 - 6p)
Answer:
2p-1
Step-by-step explanation:
Answer:
-2p - 1
Step-by-step explanation:
-4p - (1 - 6p)
-4p - 1 + 6p
-4p + 6p - 1
-2p - 1
Please let me know if I'm wrong!
I will give Brainliest.
graph the line representing the equation 10x + 12y = 240.
Answer:
Step-by-step explanation:
10x + 12y = 240 simplified is y= -5/6 +20
The x-intercept is located at ( 24 ,0)
The y-intercept is located at (0, 20)
The slope of the line represented by this equation is -5/6
Answer:
Step-by-step explanation:
The holcombe family went out to dinner the meal cost 54.65 the sales tax is 8 peecent the tip was 18 percent of the meal and tax there are 5 people in the holcomebe family what was the cost per person for the meal including sales tax and tip
Answer:
13.93
Step-by-step explanation:
Meal = 54.65
Sales tax = 8%
= 8/100 * 54.65 + 54.65
= 0.08 * 54.65 + 54.65
= 4.372 + 54.65
= 59.022
Tip = 18% of the meal and tax
= 18/100 * 59.022 + 59.022
= 0.18 * 59.022 + 59.022
= 10.62396 + 59.022
= 69.64596
Total people in the holcomebe family = 5
Cost of meal per person =
69.64596 / 5
= 13.929192
Approximately 13.93
To decorate his bedroom, Jesse spent $112.65 on new furniture, $29.75 on paint, and $48.33 on accessories. About how much did he spend to decorate his bedroom?
$170
$190
$210
$230
Answer:
$190
Step-by-step explanation:
used the calculator!
Answer: B: 190 dollars
Step-by-step explanation: This is relatively simple, but lets walk through it. First, take out the cents and add them separatly,
75
65
33
You get 1.73!
Now, add the large numbers,
112
29
48
You get 189!
Add these and get 190.73! All you need to do now is round to the nearest given answer, and you get 190 dollars!
Hope this helps, if not, comment down below please!!!
Reflect
1. When you move the decimal point, how can you know whether you are
increasing or decreasing the number?
Answer:
If u divide a number the number will decrease
if u multiply the decimal number it will increase.
when multiplying u move the decimal point to the right
if u r dividing u move the decimal point left
how much u move depends on the number of zeros from the number u are dividing or multiplying
Step-by-step explanation:
What is the mean for the data shown in the line plot?
8
6
5
5 and 7
Answer:
6
Step-by-step explanation:
its the middle
Answer:
6
Step-by-step explanation:
Find the value of w. (5w+3)
The solution is: in the expression (5w+3) the value of w is: w = -3/5.
Here, we have,
given that,
the expression is: (5w+3)
now, we have to find the value of w
so, we get,
we can find the value of w by making it equal to 0:
5w+3 = 0
<- subtract 3 from both sides
5w = -3
<- divide 5 from both sides
5w/5 = -3/5
so, we have,
w = -3/5 is the final answer.
Hence, The solution is: in the expression (5w+3) the value of w is: w = -3/5.
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sorry if it’s hard to read but can anyone help me with number 18?
Answer:
14
Step-by-step explanation:
Josh swam 25 laps in 50 minutes. At that rate, how long will it take to swim 35 laps?
Answer:
70 Minutes
Step-by-step explanation:
Divide 25 into 50 to get 2 and then multiply 2 x 35 to get 70
64 ft of rope weighs 20 pounds 28 ft of rope weighs x pounds
Answer
89.6
Step-by-step explanation:
Each foot of rope weighs 3.2 so then mutiplied 3.2 by 28 and got that
pls pls pls pls help im helpless idk what to doo or how pls helppp ill mark brainliest
1. Simplify−3+(5+3)
2. Evaluate3|2+5|+2|3−2|+ 43; = −1
3. You are renting a beach house for the summer. The cost of renting the beach house plus the one-time security deposit is represented by the equation = 151 + 575, where x represents the number of days that the beach house is rented and y is the total cost of the rental. What is the cost of the security deposit?
4. Write an expression that represents the perimeter of the rectangle.
one side is 32 and the bottom is 4 − 7
Solve each equation for the indicated variable.
5. 3−4=12 for y
6. =2+1 h for h
Match the property of real numbers illustrated by the equation.
7. 4.5(1.2 ∙ 6.7) = (4.5 ∙ 1.2) ∙ 6.7
8. 9+√2=√2+9 9. ∙1=
10.3 ∙ 4 = 1 43
11.2( + ) = 2 + 2
A. Inverse Prop. Of Multiplication
B. Distributive Prop.
C. Associative Prop. Of Multiplication
D. Identity Prop. Of Addition
E. Commutative Prop. Of Addition
Write an algebraic expression to model each situation.
12. the product of 8 and the sum of a number x and 3
13. The piggy bank contained $35 and you added $2.75 each day
14. You spent $45 on pencils, calculators, and rulers. Pencils (p) cost $2, calculators (c) cost $25, and rulers (r) cost $4, each.
Solve each inequality and graph the solution.
15. 2−5≥−23
16. −30 4−1 Or 3 > −4 + 15
Solve the absolute value equations and check for extraneous solutions.
18. |5−2|=9 Case 1: (Positive) (5 − 2) = 9 Case 2: (Negative) −(5 − 2) = 9
19.|2 − 8| = −4 − 2 Case 1: (Positive) Case 2: (Negative)
Solve the absolute value inequality and graph the solution.
20.6| − 4| ≤ 48 Case 1: (Positive) 6( − 4) ≤ 48 Case 2: (Negative) 6(−( − 4)) ≤ 48
Answer:b
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
IN
19. 5x + 7 < 2x + 1
How to solve
Answer:
x < - 2
Step-by-step explanation:
Step 1:
5x + 7 < 2x + 1 Equation
Step 2:
3x + 7 < 1 Subtract 2x on both sides
Step 3:
3x < - 6 Subtract 7 on both sides
Step 4:
x < - 6 ÷ 3 Divide
Answer:
x < - 2
Hope This Helps :)
what determines the range of a function?
Answer:
all possible y values
Step-by-step explanation:
any y value that goes in the function is in the range , an easier way to determine that would be using graphs.
why are there two values of theta if tan theta = 0.4226
Answer:
[tex]22.91^\circ, 202.91^\circ[/tex]
Step-by-step explanation:
Given that:
[tex]tan\theta=0.4226[/tex]
To find:
The two values of [tex]\theta = ?[/tex]
Solution:
By given equation:
[tex]\theta = tan^{-1}(0.4226)[/tex]
[tex]\theta[/tex] can be equal to [tex]\approx 20.91^\circ[/tex]
Also, we know the property that, [tex]tan\theta[/tex] is positive in the 3rd quadrant.
and following is also true:
[tex]tan\theta = tan(180^\circ+\theta)[/tex]
Therefore, another value possible for [tex]\theta[/tex] can be:
[tex]\theta =180^\circ+22.91\\\Rightarrow \theta \approx 202.91^\circ[/tex]
Therefore, the answer is:
[tex]22.91^\circ, 202.91^\circ[/tex]
Help and hurry please!!
In the 2000 Summer Olympics, Michael Johnson ran the 400-meter race in 43.84 seconds. To the nearest hundredth, what was his speed in meters per second?
a.
9.12 m/s
c.
1.09 m/s
b.
10.96 m/s
d.
91.24 m/s
Please select the best answer from the choices provided
a
Step-by-step explanation:
Help hurry need to turn in soon
Answer: x = [tex]\frac{-z - 7}{y}[/tex]
Step-by-step explanation:
Flip the equation
xy + z = −7
Add -z to both sides
xy + z + −z = − 7 + −z
xy = −z − 7
Divide both sides by y
[tex]\frac{xy}{y}[/tex] = [tex]\frac{-z - 7}{y}[/tex]
x = [tex]\frac{-z - 7}{y}[/tex]
x = [tex]\frac{-z - 7}{y}[/tex]
All of the following statements are true, except . . .
The product of a and c is negative.
The product of b and c is positive.
The product of b and 0 is 0.
The product of a and b is positive.
Answer:
The product of b and c is positive.
Step-by-step explanation:
b is negative as its less than 0
c is > 0 and is thus positive
multiply these would be negative result
Answer:
The product of b and c is positive.
Step-by-step explanation:
had this question
d. How many dozen doughnuts are there in 46.2 doughnuts?
Answer:
3.85
Step-by-step explanation:
46.2/12=3.85
Answer:
3.85 dozens of doughnuts
Step-by-step explanation:
well first of a dozen equals 12
dozen = 12
and if you have 46.2 doughnuts then you would divide that be 12
46.2 / 12 = 3.85
46.2 doughnuts is equal to 3.85 dozens
Which of the following is a valid triangle congruence theorem?
AAA
SSA
ASA
none of the above
The valid triangle congruence theorem is ASA.
ASA representing Angle Side Angle and means that we have two triangles
where we know two angles and the included side are equal.
This theorem states that If two angles and the included side of one triangle
are equal to the corresponding angles and side of another triangle, the
triangles are congruent.
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help pls I'm not smart enough for this..
Answer:
y = 1/2x, 2:1y = 5x, 1:5y= 1.5x, 16:24y = 3x, 1:3Step-by-step explanation:
Number replaces with each corresponding value.
The number on the left is the x, and the number on the right of the colon is y.
Simply replace x and if you get the y, it is a match.
y = 1/2(2) = 1
y = 5(1) = 5
y = 1.5(16) = 16
y = 3(1) = 3