Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
Answer:
[tex]A) \ \{ \dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2} \}[/tex]
Step-by-step explanation:
The quadratic equation to be solved is presented here as follows;
x² + 3·x - 5 = 0
The quadratic formula for a quadratic equation of the form, a·x²+b·x + c = 0, where 'a', 'b', and 'c' are constants and 'x' is unknown, is given as follows;
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4 \cdot a \cdot c} }{2 \cdot a}[/tex]
By comparison with the given equation, we have;
a = 1, b = 3, and c = -5
By plugging in the values, we get;
[tex]x = \dfrac{-3 \pm \sqrt{3^2 - 4 \times 1 \times (-5)} }{2 \times 1}[/tex]
Therefore;
[tex]x = \{\dfrac{-3 + \sqrt{9 + 20} }{2}, \dfrac{-3 - \sqrt{9 + 20} }{2}\} = \{\dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2}\}[/tex]
[tex]x= \{\dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2}\}[/tex]
Related Questions
Manny begins his new job on Monday. He will work 8 hours each day and will be paid $10.50 for each hour that he works.
Part A: How many days will Manny need to work in order to earn $2,100?
Part B: If Manny works 5 days each week, how many weeks will he need to work in order to earn $2,100?
Answers
2100 divided by 10.50 = 200 hours
200 hours divided by 8 hour days = 25 days
Answer:
A) 25 days
B) I got 4.6 so try 4 and 5 and 4.6
Step-by-step explanation:
A) 8x10.50=84
2100/84=25 days
B) 84x5=450
2100/450=4.6
is y= 4/5x -8 and y -= -5/4x = +3 parallel perpendicular or neither
Answers
Answer:
perpendicular
Step-by-step explanation:
perpendicular if the product of their slopes is equal to -1
Parallel lines have equal or identical slopes
A kite is shaped like an isosceles triangle. To the nearest tenth what is the length of the spine?
Answers
Answer: 73.2
Step-by-step explanation:
78/2 is 39. Now, use the pythagorean theorem to find the hypoteuse (in this case the spine), which is about 73.2
It’s for my other question
Answers
Answer:
That looks good
Step-by-step explanation: wait why is this here?
Is the triangle with sides of length 5 cm 3 cm and 4 cm a right angled triangle If yes why?
Answers
The triangle with sides of length 5 cm 3 cm and 4 cm is a right angled triangle because (3, 4, 5) is a Pythagorean triple.
We know that if non zero real numbers a, b, c follows Pythagoras theorem c² = a² + b², the numbers a, b, c is called as a Pythagorean triple.
And these numbers are nothing but the sides of right triangle.
Here we have been given the triangle with sides of length 5 cm 3 cm and 4 cm
Assume that p = 5 cm, q = 3 cm and r = 4 cm
p² = 25
q² = 9
and r² = 16
Consider q² + r² = 16 + 9
q² + r² = 25
q² + r² = r²
Since given numbers follows Pythagoras theorem, (3, 4, 5) is a Pythagorean triple.
And p = 5 cm, q = 3 cm and r = 4 cm are the lengths of sides of right triangle.
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Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
Four hemispheres are present in the shaded area. One large hemisphere and three smaller hemispheres each have a radius of 18 cm.
What is the perimeter of the hemisphere's formula?Consequently, the hemisphere's total surface area is 3(pi)R2. A semicircle has a curved line and a straight line that are both equal to the circle's diameter. The curving line is 2R in length while the straight line is (pi)R in length. So, 2R + (pi)R is the semicircle's total perimeter.
The shaded regions' area is calculated as follows:
initially, area of a hemisphere = 2r2 square units
the area of three small hemispheres
(2*3.14*6 r).3 = 226.08 cm2
Area of the larger hemisphere
2*3.14*18^2 = 2034.72cm^2
Total area of the shaded regions = 226.08 + 2034.72 = 2260.8cm^2
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(-2.04)(4.08) =
A)
8.3232
B)
2.04
-2.04
D)
-8.3232
Answers
Answer:
The correct answers is -8.3232
Step-by-step explanation:
N is an integer such that
3n+4 <19 and 10n/n^2+16Find all the possible values of n.
Answers
N is the integer between {3,4,5}.so we can find all possible values of n is 2 and 8.
What is an integer?An integer is a whole number that can be positive, negative or zero. Examples of integers are -5, 1, 5, 8, 97, and 3,043.The integers are generated from the set of counting numbers and the operation.
What are the steps to solving inequalities?Subtract the same number from both sides. Multiply both sides by the same positive number. Divide both sides by the same positive number. Multiply both sides by the same negative number and reverse the sign.
Now we solve
3n+4 <19
3n+4-4<19-4
3n<15
n<5
so n is less than and equal to 5 it will be {3, 4, 5].
10n/[tex]n^{2}[/tex]+16 >1
10n> [tex]n^{2}[/tex] +16
0> [tex]n^{2}[/tex]-10n +16
0>[tex]n^{2}[/tex] -8n -2n +16
0> n(n-8)-2(n-8)
0> (n-8) (n-2)
So n-2<0 n-8<0
n<2 n<8
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(I’ll give brainiest) what should you do to solve the equation x-3=12
A) add 3 to both sides
B) subtract 3 from both sides
C) divide both sided by 3
D) multiply both sides by 3
(If you can, please explain how)
Answers
Answer:
its A
Step-by-step explanation:
Find the percent decrease from 133 to 120. Round your answer to the nearest tenth
Answers
Answer:
Approximately - 9.7%
Step-by-step explanation:
By using the percent change formula, you will be able to calculate the percent decrease.
(b-a)/a times 100 <-- (percent change formula)
(120-133)/133 times 100
-13/133 times 100
-9.7744%
Answer:
9.8% decrease
Step-by-step explanation:
You want the percent decrease from 133 to 120.
Percent changeThe amount of change as a percent can be found using the formula ...
percent change = ((new value)/(old value) -1) × 100%
Here, the new value is 120, and the old value was 133. The change is ...
percent change = (120/133 -1) × 100% ≈ (0.90226 -1) × 100%
= -0.09774 × 100% ≈ -9.8%
The change from 133 to 120 is a 9.8% decrease.
__
Additional comment
When the sign of the change is negative, as here, the change is a decrease. If the sign is positive, the change is an increase. That is, a change of -9.8% is a 9.8% decrease. (You can use either the minus sign or the word "decrease" to indicate the direction of the change. The acceptable form of the answer will depend on your grader.)
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How many 4 digit multiples can not be divided by 5
Answers
Answer:
1800
Step-by-step explanation:
Let us solve this question by Modular Airthmatic.
Let the lowest 4 digit number be X.
X= 1 (mod 5)
X =2 (mod 5)
X=3 (mod 5)
X =4 (mod 5)
X=1+5 t where t is any integer.
1+5 t=2 (mod 5)
5 t=1 (mod 5 )
5 is the Modular Inverse of modulo 5
t=1 (mod 5)
t =1+5 u : u= any integer.
X becomes 1+ 5 (1+5u )=6+25 u
6+25u =3 (mod 5)
25 u= -3 (mod 5)=2 (mod 5)
25 is Modular Inverse of Modulo 5
u=2 (mod 5)
u =2+5 v : v= any integer.
X becomes 6 +25 (2+5 v)=56+125 v .
56 +125 v=4 (mod 5)
125 v=-52 (mod 5)=3 (mod 5)
125 is Modular Inverse of modulo 5
v = 3 (mod 5)
v =3 +5 w where w is any integer.
For lowest 4 digit number, take
w=200
X=1003 : Lowest 4 digit number.
Take w=201
X=208 : Next number.
For 4 digit largest number, take
w=1995
X= 9978 : Largest number.
No. of Numbers =(1995 - 200 )+1=1800 □Ans.
Answer:
1800 ways.
Step-by-step explanation:
Does the equation y=x/2 represent a proportional relationship?
Answers
1. If Jose says that 75% of his class of 28 students
rides the bus every day, how many students ride
the bus?
a. 25
b. 15
C. 21
(d. 10
Answers
75% of 28
Convert the percent to a decimal
75/100=0.75
0.75(28)
21
answer: C
Which inequality statement describes the two numbers on a number line? "−13 and a number 18 units to the right of −13"
A) −13 < 5
B) −13 > 5
C) −13 > 18
D) −13 < 18
Answers
Answer:
A
Step-by-step explanation:
-13 + 18=5
-13 is less than 5
Reasonable Time: Algorithms with a polynomial efficiency or lower (constant, linear, square, cube, etc.) are said to run in a reasonable amount of time. Unreasonable Time: Algorithms with exponential or factorial efficiencies are examples of algorithms that run in an unreasonable amount of time. Your school is considering running the group raffle at an upcoming assembly to give away a prize. Write a brief explanation of what advice you would give them.
Answers
Unreasonable Time is the nest option for running the group raffle at an upcoming assembly to give away a prize.
As given that;
Reasonable Time: Algorithms with a polynomial efficiency or lower (constant, linear, square, cube, etc.) are said to run in a reasonable amount of time.
Unreasonable Time: Algorithms with exponential or factorial efficiencies are examples of algorithms that run in an unreasonable amount of time.
Your school is considering running the group raffle at an upcoming assembly to give away a prize.
We have to write a brief explanation of what advice you would give them.
We can use the unreasonable time because running the group raffle at an upcoming assembly to give away a prize cannot complete their work is the given amount of time.
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In circle K shown below, points B, C, D, and E lie on the circle with secants HBD and HCE drawn. Prove:
HExDC=HDxEB
Answers
Answer:
By exterior angle theorem, we have;
∠DBE = ∠H + ∠HEB = ∠ECD = ∠H + ∠HDC
∴ ∠H + ∠HEB = ∠H + ∠HDC
By addition property of equality, we have
∠HEB = ∠HDC
∠H = ∠H by reflexive property
∴ ΔHCD ~ ΔHEB by Angle Angle AA similarity postulate
∴ HE/HD = EB/DC, by the definition of similarity
Therefore, by cross multiplication, we have;
HE × DC = EB × HD
Therefore, by commutative property of multiplication, we have;
HE × DC = HD × EB
Step-by-step explanation:
How many one-cup servings of milk are in a two-liter bottle? Round your answer to the nearest tenth.
____________one-cup servings
Answers
Answer: 10.56 cups.
Step-by-step explanation:
1 liter = 4.22 cups; 1.5 liters = 6.34 cups; 2 liters = 8.45 cups; 2.5 liters = 10.56 cups.
what is the x-intercept of the graph of the equation 3x-4y=20
Answers
Answer:
(20/3,0) is your x-intercept
Step-by-step explanation:
To find x-intercept, let y = 0
[tex] \displaystyle{3x = 20}[/tex]
Solve for x, divide both sides by 3:
[tex] \displaystyle{ \dfrac{3x}{3} = \dfrac{20}{3}} \\ \\ \displaystyle{ x = \dfrac{20}{3}}[/tex]
Hence, the x-intercept is (20/3,0). We write in order pair since it's x-intercept and x = 20/3 at y = 0
Which scenario is modeled by this graph?
Answers
Answer:
The first option seems about right
if N(U) = 65, N(A)=28 N(B)= 45 and N(ABC)= 20 then N(AUB) is ?
Answers
Answer:
98--(&_$4567;'#234678
Answer:
N(AUB)=28+45
=73
Step-by-step explanation:
trigonometry PLEASE HELP ASAP TYY
Answers
Answer:
x = 3.1
Step-by-step explanation:
Begin with the right triangle on the left. Looking at the 39° angle, the 7m side is the hypotenuse and the side marked h (see attached image) is the opposite side. The trig ratio using opposite and hypotenuse is sine.
[tex]\sin{39^\circ}=\frac{h}{7}\\\\h=7\sin{39^\circ}[/tex] Hold this thought!
Focus attention on the right triangle on the right. Looking at the 55° angle, h is the opposite side and the side marked x is the adjacent side. The trig ratio using opposite and adjacent sides is tangent.
[tex]\tan{55^\circ}=\frac{h}{x}\\\\x\tan{55^\circ}=h\\x\tan{55^\circ}=7\sin{39^\circ}\\x=\frac{7\sin{39^\circ}}{\tan{55^\circ}} \approx 3.1[/tex]
q significa I love you?
Answers
The following shape is a rhombus, solve for the value of x.
Answers
Answer: The answer is -1.6
Step-by-step explanation:
(7x-5)=2x-13
+5 +5
7x=2x-8
5x=-8
divide -8 by 5= -1.6
Answer:
-1.6
Step-by-step explanation:
24 water bottles for $2.95
Answers
The cost of 48 water bottles will be $5.9.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that there are 24 water bottles and costs $2.95. The cost of 48 water bottles will be calculated as,
24 water bottles = $2.95
1 water bottle = $2.95 / 24
48 water bottle = ( 2.95 x 48 ) / 24
48 water bottles = $5.9
Hence, the cost will be $5.9.
The complete question is given below.
24 water bottles for $2.95. What is the cost of 48 water bottles?
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Given the answer for part D, write an expression that will tell you the direction the robot is going if, in the course of its journey, it turns left 21 times and turns right 22 times. Does the order the robot makes the turns in matter for the purpose of knowing the direction it is finally facing?
The answer to part D is in the picture...
Answers
The robot is moving in the direction indicated by the formula ((i)²¹*(-i)²²)d, or in the beginning direction.
What is complex plain?
When a line is rotated in the complex plane either clockwise or anticlockwise, it is multiplied by -i or I depending on which direction the line is rotated. The direction vector is rotated 90 degrees in the clockwise direction to make a right turn. It is the same as increasing the complex number by -i.
A left turn is represented as a 90° anticlockwise rotation of the direction vector. It is comparable to increasing the complex number by i.
There are 21 left turns of the robot. The direction vector will now be di21. Once it has been rotated 22 times to the right, the direction vector will now be (di²¹)*(-i)²²=d((i)²¹*(-i)²²).
Consequently, the robot's current direction is:
d((i)²¹*(-i)²²)= di²¹⁺²²=di⁴³= d(-i)= -di
No matter what, the direction will always be the same, hence the sequence is irrelevant.
Hence, the equation that will indicate where the robot is moving is ((i)²¹*(-i)²²)d, or in the starting direction. Furthermore, the final direction it faces does not depend on the order.
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For what value of a the system of linear equations Ax 3y a 3 12x ay A has no solutions?
Answers
The system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.
To determine if the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a, we can use the elimination method.
We want to eliminate one of the variables, so let's start by multiplying the first equation by 3 and the second equation by -1.
This gives us:
3Ax + 9y = 3a, -3x - ay = -A.
Now we add the equations together to get:
2Ax + 8y = 3a - A.
Now we can see that the equation is not solvable as there is no value of a that will make the equation true. Therefore, the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.
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How many times would you expect to roll a 5 if you rolled a fair die 1,300 times? Round your answer, if needed.
A.
0.1667
B.
1,083
C.
217
D.
95
Answers
Answer: C, 217
Step-by-step explanation:
Beth is making a garden plot which measures 6 open parentheses square root of x plus 2 end root close parentheses units in length and open parentheses 5 square root of x plus 2 end root close parentheses units in width. What is the area of the garden?
Answers
The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.
What is the area of the garden plot whose length and width are as described?It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.
Recall that Area, A = length × width.
Therefore, since length = 6 (√(x + 2)) units
The width = (5 √(x + 2) ) units
Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )
= 30 (x + 2) square units
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A bag contains 18 red marbles. The ratio of red marbles to blue marbles is 6 to 9. Find the number of blue marbles in the bag.
Answers
Giving brainly to who ever answers first.
Answers
Answer:
1/9 for left
15/16 for second
Step-by-step explanation:
1/3 x 1/2 x 2/3 = 1/9
5/4 x 3/2 x 1/2 = 15/16
Answer:
[tex]\frac{1}{9}[/tex] m³
[tex]\frac{5}{16}[/tex] ft³×÷
[tex]3\frac{1}{8}[/tex] m³
[tex]12\frac{1}{2}[/tex] m³
x = 20 in.
l = 10 in.
Step-by-step explanation:
[tex]2\frac{4}{5}=\frac{14}{5}[/tex]
[tex]1\frac{3}{7}=\frac{10}{7}[/tex]
[tex]3\frac{1}{8}=\frac{25}{8}[/tex]