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
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
Peter says, "If you subtract 13 from my number and multiply the difference by -3, the result is
- 69." What is Peter's number?
Answer:
Peter's number is 36.
Step-by-step explanation:
If you subtratct 13 from 36, you get 23.
If you multiply that times -3, you get -69.
(The way I got 23 was by dividing -69 and -3)
I hope this helped you even though it's late.
Does this image have a vertical reflection, horizontal reflection, and rotation? I'll give brainiest!
Answer:
Reflection with respect to the x axis
Step-by-step explanation:
Reflection with respect to the x avis, or horizontal reflection.
INDEPENDENT PRACTICE
A rotating sprinkler spins and shoots water out a distance of 9 feet. What is the approximate area that is
being watered by the sprinkler?
A. 28 ft?
B. 80 ft
9 ft
C. 154 ft?
D. 254 ft?
Madyson goes to a restaurant with her best friend, Taylor. The two girls order a meal, Madyson's meal costs $23.75 and Taylor's meal is $15.00. They want to leave a tip of 15% how much money would it cost altogether without tax?
Answer:30.75
$23.75 +$15.00=30.75
5+3=6
21=3
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.
read more: https://brainly.com/question/18676144?referrer=searchResults
sorry if it’s hard to read but can anyone help me with number 18?
Answer:
14
Step-by-step explanation:
help plz idk it ughhhhhhhhhhhhh
Answer:
20.4
Step-by-step explanation:
136 × 0.85% =
136 - 115.6 =
20.4
Is x = 1 a solution of the equation 2 – 8x = –6?
Let's verify by substituting 1 to x.
2 - 8x = -6
2 - 8(1) = -6
2 - 8 = -6
-6 = -6
It is equal, therefore x = 1 is the solution.
Answer:
yes
Step-by-step explanation:
Substitute x = 1 into the left side of the equation and if equal to the right side then it is a solution.
2 - 8(1) = 2 - 8 = - 6 = right side
Thus x = 1 is a solution of the equation
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!!!
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:
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The lengths of two sides of the triangle are 13 feet and 23 feet. Find the possible lengths of the third side.
Answer:
Between the lengths of 10 and 36 (exclusive).
Step-by-step explanation:
Since the lengths of any two sides is always greater than the third, the shortest possible length of the third side must be greater than 23 when added to 13. 23-13 = 10, so the third side must be greater than 10.
However, the third side also cannot exceed the length of the sum of the other two sides. 23+13 = 36, therefore the length must be less than 36.
The possible lengths of the third side lie between 10 and 36 (exclusive).
If we use 'l' for length, this range can be represented as follows:
[tex]10 < l < 36[/tex]
Hope this helped!
Help me please !!!!!!!!
Answer: Since x is 157 degrees the missing value,m, is 23 degrees because a line is 180 degrees, n is also 23 degrees so it would be the same
Step-by-step explanation:
Decide whether or not each equation represents a proportional relationship. A.The remaining length (L) of 120-inch rope after x inches have been cut off: 120−x=L b.The total cost (t) after 8% sales tax is added to an item's price (p): 1.08p=t c.The number of marbles each sister gets (x) when m marbles are shared equally among four sisters: x=m4 d.The volume (V) of a rectangular prism whose height is 12 cm and base is a square with side lengths s cm: V=12s2 Problem 3
Answer and Step-by-step explanation: An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same. For example, in general:
Equation: y = mx
[tex]\frac{y}{x}[/tex] = m
m is a constant value, which means is the same.
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
[tex]\frac{t}{p}=1.08[/tex]
C. Equation: [tex]x=\frac{m}{4}[/tex]
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
[tex]\frac{m}{x}=4[/tex]
D. Equation: [tex]V=12s^{2}[/tex]
This equation is NOT proportional because side length is squared, so it is not constant linearly.
Answer:
Step-by-step explanation:
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
C. Equation:
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
What is the solution for the equation 6x - 8 = 4x? x =
Answer:
x = 4
Step-by-step explanation:
6x - 8 = 4x
subtract 4x from both sides of the equation
6x - 4x -8 = 4x - 4x
2x - 8 = 0
add 8 to both sides of the equation
2x - 8 + 8 = 0 + 8
2x = 8
divide both sides of the equation by 2
2x/2 = 8/2
x = 4
Answer:
x = 4.
Step-by-step explanation:
6x - 8 = 4x
6x - 4x - 8 = 0
6x - 4x = 8
2x = 8
x = 4.
The probability that a randomly-selected person at a show has seen the band play live before is 50%. A "superfan" is defined as someone who has seen the band play live at least 5 times. The probability that a person at a show is a "superfan" is 30%. Two people are selected at random. What is the probability that both people have both seen the band perform live before, and are "superfans?"
Answer:
0.25 and 0.09
Step-by-step explanation:
The probability that a randomly-selected person at a show has seen the band play live before is 50%=0.50
The probability that a person at a show is a "superfan" is 30%=0.30
Two people are selected at random.
The probability that both people have both seen the band perform live before
= The probability that the first person has seen the band live before and the second person also has seen the band live before.
=0.50 x 0.50
=0.25
Similarly, the probability that both are "superfans"
=The probability that the first person is a superfan and the probability that the second person is a superfan.
=0.30 x 0.30
=0.09
Hence, the probability that both people have both seen the band perform live before, and are "superfans" are 0.25 and 0.09 respectively.
us
How many milliliters are in
12 teaspoons?
1 tsp = 5 mL
12 tsp = [?] mL
Enter
Solve the equation please!!!!!
Determine the y-intercept of the following parabola:
y = 3x2 - 12x - 5
Answer:
-5
Step-by-step explanation:
Find the y-intercept by plugging in x = 0:
y = 3x^2 - 12x - 5
y = 3(0^2) - 12(0) - 5
y = 0 - 0 - 5
y = -5
(0, -5)
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
easy questions pls help (question in picture)
Answer:
1. P= 80
60/.75=80
2. x= 5/3
-27/25x / -27/25= -9/5 / -27/25
-9/5 / -27/25 --- -9/5 x -25/27
3. -300
-2.7/-2.7 = 810/-2.7
4. 120
84x100/70
84/x = 70/100
1. p=80
=(60×4)÷3
=240÷3
=80
2.x=1.6667
={-9/5}×{-25/27}
=1.6667
3.t=-300
=(810÷-2.7)
=(810×10)÷(-2.7×10)
=(8100÷(-27)
=300
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 first integer is
A. 1
B.0
C.-1
D.None of the above
Answer:
a
Step-by-step explanation:
Answer:
its B
Step-by-step explanation:
Will give Brainliest, like, comment and 10 points to best answer
Could you help me with this please?
Answer:
You are simply dividing a by 3 to reach y each time!
Step-by-step explanation:
2.(03.01)
The range of the following relation R {(3,-2), (1, 2), (-1,-4), (-1, 2)} is (1 point)
O {-1, 1, 3}
O {-1,-1, 1, 3}
O {-4, -2, 2, 2)
O {-4, -2, 2}
I will mark as brainliest
Answer:
{-4,-2,2}
Step-by-step explanation:
Please help me with these questions! Legit answers only please!
Answer:
Values of y are:
2 1 -1
2 -1 -4
Vijay’s wages were increased from £115 per week to £130 per week.
What was the percentage increase to one decimal place?
NO SILLY ANSWERS OR REPORT!
Answer:
13%
Step-by-step explanation:
The percentage decrease is calculated by the formula below;
( new value - old value)old value * 100%
old value is 130
new value is 115
So the percentage increase will be;
(130-115)/115 * 100%
= 15/115 * 100% = 13.043%
To one decimal place, this is 13%
If 1 gallon of orange juice cost 6.25. How much does it cost for 128 ounces of oj?
Answer:
$6.25
step-by-step explanation:
a gallon of oj coat 6.25
there are 128 ounces in a gallon
so 6.25 for 128 ounces is just a gallon
so 128=1 gallon. so its just $6.25
Rewrite each expression in its equivalent form.
8pq - 3pq
ASAP PLZ HELPPP
Answer:
i believe its 5pq
Step-by-step explanation:
if you do the math of it it should still be the same
Answer:
5pq
Step-by-step explanation:
Step 1: Write expression
8pq - 3pq
Step 2: Combine like terms.
Since both have a pq term in it, we can simply subtract.
8 - 3 = 5
5pq