There are four real roots for the quadratic-like equation x⁴ + 9 · x² - 10 = 0: x₁ = + √(- 9 / 2 + 11 / 2), x₂ = + √(- 9 / 2 - 11 / 2), x₃ = - √(- 9 / 2 + 11 / 2) and x₄ = - √(- 9 / 2 - 11 / 2)
How to solve a quadratic-like equation by factoring
In this problem we find a quadratic-like equation of the form a · x²ⁿ + b · xⁿ + c = 0, where a, b, c are real coefficients and whose roots must be found. This can be done by completing the square and clear variable x. First, write the polynomial:
x⁴ + 9 · x² - 10 = 0
Second, use the following substitution: u = x²
u² + 9 · u - 10 = 0
Third, complete the square:
u² + 9 · u + 81 / 4 = 10 + 81 / 4
u² + 9 · u + 81 / 4 = 121 / 4
Fourth, factor the expression and clear variable u:
(u + 9 / 2)² = 121 / 4
u + 9 / 2 = ± 11 / 2
u = - 9 / 2 ± 11 / 2
Fifth, reverse the substitution and clear variable x:
x² = - 9 / 2 ± 11 / 2
x = ±√(- 9 / 2 ± 11 / 2)
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To get to the baseball game, Todd drove 2 hours and 10 minutes, stopped for 15 minutes, then drove 1 hour 15 minutes more to get to the game. If he arrived at 6:10, what time did he leave?
(2x)⁴ = (2x)(2x)(2x)(2x)
(xy)⁷ =
(-ab)⁶ =
write in expanded form
Step-by-step explanation:
(xy)(xy)(xy)(xy)(xy)(xy)(xy)
(-ab)(-ab)(-ab)(-ab)(-ab)(-ab)
7 times the sum of 3 and q
one-fourth of z is subtracted from 6
Answer:
7(3+q)
(Z)/(1/4) - 6
The length of a rectangle multiplied by 3 is equal to 4 times its width. The perimeter is 8 2/5 feet. Find the length and width.
Answer:
W=1 4/5 feet
L= 2 2/5 feet
Step-by-step explanation:
3L = 4W L = 4W/3
2L+2W = 8 2/5
Substitute L
2(4W/3)+2W = 8 2/5
8W/3+2W = 8 2/5
multiply both sides by 3
8W+6W = 24 6/5
14W = 25 1/5
Divide both sides by 14
14W/14 = (25 1/5)/14
W = (126/5)/14 = 9/5 = 1 4/5
Substitute for W
L = 4(1 4/5)/3
L = (4)(9/5)/3 = (36/5)/3 = 12/5 = 2 2/5
The perimeter is an enclosed area of any two or one-dimensional shape.
The perimeter of a rectangle is given by:
[tex]\rm P = 2 ( L + B )[/tex]
The length is [tex]\rm 2 \dfrac{2}{5} feet[/tex] and the width of the rectangle is [tex]\rm 1\dfrac{4}{5} feet[/tex].
This can be calculated by:
Given,
Perimeter (P) = [tex]\rm 8 \dfrac{2}{5} feet[/tex]Let,
Length = LWidth = WSince,
3L = 4W
[tex]\rm L = \dfrac{4W}{3}[/tex]
Substituting the value of L in the equation of perimeter:
[tex]\rm 2(\dfrac{4W}{3}) + 2W = 8 \dfrac{2}{5}[/tex]
[tex]\rm \dfrac{8W}{3} + 2W = 8 \dfrac{2}{5}[/tex]
Now multiplying the left and right sides by 3 we get:
[tex]\rm 8W+6W = 24 \dfrac{6}{5}[/tex]
[tex]\rm 14W = 25 \dfrac{1}{5}[/tex]
Now divide both sides by 14:
[tex]\rm \dfrac{14W}{14} =\dfrac{(25 \dfrac{1}{5})}{14}[/tex]
[tex]\rm W = \dfrac{(\dfrac{126}{5})}{14} \\\\= \dfrac{9}{5}[/tex]
[tex]\rm W = 1 \dfrac{4}{5}[/tex]
Now substituting the value of W, length can be calculated:
[tex]\rm L = \dfrac{4(1 \dfrac{4}{5})}{3}[/tex]
[tex]\rm L = \dfrac{(4)\dfrac{9}{5}}{3} \\\\= \dfrac{(\dfrac{36}{5})}{3} \\\\= \dfrac{12}{5}[/tex]
[tex]\rm L = 2 \dfrac{2}{5}[/tex]
Therefore, length is [tex]\rm 2 \dfrac{2}{5} feet[/tex] and width is [tex]\rm 1\dfrac{4}{5} feet[/tex].
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This is the equation
5(15+3)
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
The 5 would distribute into the 15+3 so that it would be (15x5)+(3x5)
And then you would get 75+15 which is 90
Activity
Rylee shopped at a clothing store, where she spent $36.50 plus 8% tax. Then, she spent $25 to refuel her car at the gas station. Finally, she bought groceries worth $23.50. At the grocery checkout, she handed over a coupon for a 20% discount on her purchase.
Complete the following steps to help Rylee find the net change to her banking account balance.
Part B
Write an expression that represents the net change in Rylee’s bank account balance after paying for fuel at the gas station.
Part C
Use decimal numbers to write an expression that represents the net change in Rylee’s bank account balance after paying for groceries.
Part D
Finally, use decimal numbers to write an expression that represents the net change in Rylee’s bank account balance for her entire shopping trip. Use your answers from parts A through C to guide you.
Part E
Simplify the expression in part D to find the net change in Rylee’s bank account balance. Express your answer as a decimal number.
Answer:
A)
Rylee bought $36.50 in clothes. This money is leaving her bank account, so represent the amount with a negative sign: -$36.50.
The tax on her purchase is 8%, so the tax amount is 0.08 × -$36.50. The expression that represents the net change in her bank account is -$36.50 + (0.08 × -$36.50).
Further simplify the expression by factoring -$36.50 from both terms:
-$36.50 + (0.08 × -$36.50)
=
-$36.50(1 + 0.08)
=
-$36.50(1.08).
B)
Rylee spent $25 for fuel at the gas station. This money is leaving her bank account, so represent the amount with a negative sign: -$25.
C)
The original price of Rylee’s groceries was $23.50. This money is leaving her bank account, so represent the amount with a negative sign: -$23.50.
Rylee got a 20% discount on her purchase. In other words, she got 20% of her money back. The expression that represents the net change in her bank account is -$23.50 – (-$23.50 × 0.2).
Further simplify the expression by factoring -$23.50 from both terms:
-$23.50 – (-$23.50 × 0.2) = -$23.50(1 – 0.2)
= -$23.50(0.8).
D)
clothing store:
-$36.50(1.08) or -$36.50 + (0.08 × -$36.50)
gas station:
-$25
grocery store:
-$23.50(0.8) or -$23.50 – (-$23.50 × 0.2)
After adding the three expenses:
-36.5 + (-36.5)(0.08) + (-25) + (-23.5) − (-23.5)(0.2) or
(-36.5)(1.08) + (-25) + (-23.5)(0.8).
E)
(-36.5)(1.08) + (-25) + (-23.5)(0.8) = -$83.22
enjoy :)
Sarah makes 1/2 pound of caramel popcorn and puts it in a bags that hold 1/8 of a pound which equation can used to find how many bags she can fill
Answer:
1/2 ÷ 1/8 =b
Step-by-step explanation:
1.101^3 in normal form
Answer:
The answer is 1,101.
Step-by-step explanation:
1.101 ^ 2 = 11.01
And 1.101 ^ 4 = 11,010.
Which of the following is a pair of
vertical angles?
B
A
B
х
ООО
с
D
A. ZAXD and ZAXC
B. ZBXC and DXE
C. ZAXB and ZDXE
D. ZAXE and ZBXC
Answer:
B. <BXC and <DXE
Step-by-step explanation:
Vertical pair of angels are two opposite vertical angles formed when two traight lines intersect each other. They are of equal measure.
From the diagram, <BXC is vertically opposite to <DXE. Therefore they are a pair of vertical angles.
What is an
equation of the line that passes through the points (8, 5) and (-6, 5):
Answer:
y=8
Step-by-step explanation:
formula of a line equation
y=MX+c
m=Y2-Y1÷X2-X1
m=5-5÷-6-8
m=0÷-14
m=0
substitutionusing (8,5)
8=0(5)+c
8=c
Find the area of a rectangular carpet the measures 3 1/3 feet by 3 feet
Answer:
10 feet
Step-by-step explanation:
The distribution of waiting time for an elevator in an office building is shown above. What is the probability you’ll have to spend between 30 and 70 seconds waiting for the elevator?
Answer:
I don't think this question can be answered without more info
Two points are located on a graph, Point A is (-1, 10), and Point B is (4,3). What is the
distance between Point A and Point B?
A) 8.6
B)13.3
C) 10
D)3
Answer:
10
Step-by-step explanation:
I WILL MARK BRAINLEST PLS
Oki received a statement on her Certificate of Deposit showing that her investment had returned $8,000 over its life. If the Certificate of Deposit pays a simple interest rate of 4% and her initial investment was $ 20,000, how long had the money been invested?
Select one:
a. 130.1 months
b. 10 years
c. 10.8 years
d. 80 months
Answer:
b) 10 years
Step-by-step explanation:
8,000 x .04 = 800 x 10 = 8000
Hope that helps!
Answer:
10
Step-by-step explanation:
show that the function below even or odd. f(x) = 3 X5 / 1+X3
Answer:
i think the answer is
[tex]f(x) = \\ - \frac{45x {}^{2} }{(1 + x {}^{3}) {}^{2} }[/tex]
The hypotenuse of a triangle is one foot more than
twice the length of the shorter leg. The longer leg IS
seven feet longer than the shorter leg. Find the
dimensions of the triangle.
Answer:
y uwu
Step-by-step explanation: i think
The ratio of the volume of orange juice in Glass A to the volume of orange juice in
Glass B is 5: 3. Half of the orange juice in Glass A is poured into Glass B. What is the
new ratio of the volume of orange juice in Glass A to the volume of orange juice in
Glass B?
Answer: A:B = 3:13
Step-by-step explanation:
B 5, A 3 (double to get rid of halves)
B 10, A 6, —> B 13 A 3
The question needs you to find the new ratio of the glasses
The new ratio of glass A to glass B = 2.5 : 5.5
Glass A = 5
Glass B = 3
Half of the orange juice in Glass A is poured into Glass B
B = 3 + 1/2 of 5
= 3 + (1/2×5)
= 3 + 5/2
= 6 + 5 / 2
= 11/2
B = 11/2
= 5.5
A = 5 - 1/2 of 5
= 5 - (1/2×5)
= 5 - 5/2
= 10-5/2
= 5/2
= 2.5
The new ratio of glass A to glass B = 2.5 : 5.5
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the options are
A. 1
B. -1
C. 1
D. 1
someone please help with the if the domain is restricted between -2
Answer:
The awnser is c.
PLEASE HELP MUST BE AT LEAST 5 SENTENCES PLEASE HELP DUE IN 5 MINS
Answer:
I think that Thomas Clarksons motive for publishing this drawing of a slave ship was to inform people what it was like. He wanted to show how crowded it was. Thomas might have wanted to show how people were treated.
( i dunno what else to put but you could talk about how he felt about the slave trade)
How do I solve × + 12, × = 15
Answer:
27
Step-by-step explanation:
x+12
Let x=15
15+12
27
Answer:
x = 15th root of (-0.067) = -0.83482
Step-by-step explanation:
I need help please.
Answer:
A) c(x)=2x+60
$74
Step-by-step explanation:
A) c(x)=2x+60
$74
1. Which numerical expression has the value of 60?
4. (12+ 4) 3 b. 12 - 14 - 3) c.** 12 + 3)
d. 12 - 4-3
Answer:
sorry but I can't really tell if any of them have 60 it kind of looks like none of them have 60 unless theres a bit multiplying then maybe I can help but other wise right no sorry
Compare the fractions using >, < or=.
9/10 and 78/100
Answer:
9/10 > 78/100
Step-by-step explanation:
We can make 9/10 into 90/100, and since they now have the same denominator (Bottom number in fraction), we can now compare the numerators (Top number in fraction). 90 is greater than 78 so we can say that 9/10 > 78/100 (9/10 is greater than 78/100).
Find the area of the composite figure below.
2 ft
2 ft
6 ft
4 ft
8 ft
22 ft2
30 st²
36 ft²
38 ft
Answer:
A = 139.25
Step-by-step explanation:
Evaluate Square root b2 - 4ac when a = 1, b = -6, and c = 9.
Answer:
[tex]x=3[/tex]
como puedo resolver 5 anos en in minuto
A pair of shoes costs $50. What is the total cost of the shoes after 7.25% tax is added? Round the tax to the nearest cent.
Answer:
Step-by-step explanation:
50(1+7.25/100)
50(107.25/100)
50(1.0725)
53.625
$53.63
can someone help me with a two step equation that will be x=2
Answer:
i can help
Step-by-step explanation:
Answer:
Step-by-step explanation:
2
The Roller family spends $134 on 2 adult tickets and 3 youth tickets at an amusement park. The Coaster family
spends $146 on 3 adult tickets and 2 youth tickets at the same park. Find the price of adult and youth tickets,
Answer:
34 adult ticket and 22 youth tickets
Step-by-step explanation:
Let the price of adult be x
Let the price of youth tickets be y
If the Roller family spends $134 on 2 adult tickets and 3 youth tickets at an amusement park, then;
2x+3y = 134 .... 1
Also if the Coaster family spends $146 on 3 adult tickets and 2 youth tickets at the same park then;
3x+2y = 146 ..... 2
Solve simultaneously
2x+3y = 134 .... 1 * 3
3x+2y = 146 ..... 2 * 2
_____________
6x+9y = 402
6x+4y = 292
Subtract
9y-4y = 402-292
5y = 110
y = 110/5
y = 22
Substitute y =22 into 1;
From 1;
2x+3y = 134
2x+3(22) = 134
2x+66 = 134
2x = 134-66
2x = 68
x = 34
Hence there are 34 adult ticket and 22 youth tickets