Answers
The solutions of the quadratic equations are listed below:
x₁ = - 1.5, x₂ = - 2 b₁ = 3, b₂ = - 0.8 m₁ ≈ 6.702, m₂ ≈ 0.298 h₁ ≈ 3.908, h₂ ≈ - 1.408 x₁ ≈ 1.333, x₂ = - 2 n₁ ≈ 14.446, n₂ ≈ 0.554 a₁ ≈ - 0.117, a₂ ≈ - 2.133 k₁ ≈ 2.108, k₂ ≈ - 1.708 t₁ = 1.75, t₂ = - 2.5 y₁ ≈ 0.333 + i 1.491, y₂ ≈ 0.333 - i 1.491 q₁ ≈ 2.408, q₂ ≈ - 2.908 x₁ ≈ 8.273, x₂ = - 2.273How to solve a quadratic equation by using the quadratic formula
In this problem we find quadratic equations of the form a · x² + b · x + c = 0, whose roots can be found analytically by using the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c), a ≠ 0
Now we proceed to solve each quadratic equation:
1) 2 · x² + 7 · x + 6 = 0
x = - 7 / (2 · 2) ± [1 / (2 · 2)] · √(7² - 4 · 2 · 6)
x₁ = - 1.5, x₂ = - 2
2) 5 · b² - 11 · b - 12 = 0
b = 11 / (2 · 5) ± [1 / (2 · 5)] · √[(- 11)² - 4 · 5 · (- 12)]
b₁ = 3, b₂ = - 0.8
3) m² - 7 · m + 2 = 0
m = 7 / (2 · 1) ± [1 / (2 · 1)] · √[(- 7)² - 4 · 1 · 2]
m₁ ≈ 6.702, m₂ ≈ 0.298
4) 2 · h² - 5 · h - 11 = 0
h = 5 / (2 · 2) ± [1 / (2 · 2)] · √[(- 5)² - 4 · 2 · (- 11)]
h₁ ≈ 3.908, h₂ ≈ - 1.408
5) 3 · x² + 2 · x - 8 = 0
x = - 2 / (2 · 3) ± [1 / (2 · 3)] · √[2² - 4 · 3 · (- 8)]
x₁ ≈ 1.333, x₂ = - 2
6) n² - 15 · n + 8 = 0
n = 15 / (2 · 1) ± [1 / (2 · 1)] · √[(- 15)² - 4 · 1 · 8]
n₁ ≈ 14.446, n₂ ≈ 0.554
7) 4 · a² + 9 · a + 1 = 0
a = - 9 / (2 · 4) ± [1 / (2 · 4)] · √(9² - 4 · 4 · 1)
a₁ ≈ - 0.117, a₂ ≈ - 2.133
8) 5 · k² - 2 · k - 18 = 0
k = 2 / (2 · 5) ± [1 / (2 · 5)] · √[(- 2)² - 4 · 5 · (- 18)]
k₁ ≈ 2.108, k₂ ≈ - 1.708
9) 8 · t² + 6 · t - 35 = 0
t = - 6 / (2 · 8) ± [1 / (2 · 8)] · √[6² - 4 · 8 · (- 35)]
t₁ = 1.75, t₂ = - 2.5
10) 3 · y² - 2 · y + 7 = 0
y = 2 / (2 · 3) ± [1 / (2 · 3)] · √[(- 2)² - 4 · 3 · 7]
y₁ ≈ 0.333 + i 1.491, y₂ ≈ 0.333 - i 1.491
11) 2 · q² + q - 14 = 0
q = - 1 / (2 · 2) ± [1 / (2 · 2)] · √[1² - 4 · 2 · (- 14)]
q₁ ≈ 2.408, q₂ ≈ - 2.908
12) 0.5 · x² - 3 · x - 9.4 = 0
x = 3 / (2 · 0.5) ± [1 / (2 · 0.5)] · √[(- 3)² - 4 · 0.5 · (- 9.4)]
x₁ ≈ 8.273, x₂ = - 2.273
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Related Questions
logarithmic differentiation Y=2^X
Answers
By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
How to use logarithmic differentiation
Logarithmic differentiation is a combination of derivative rules and logarithm properties which is useful to derive power, exponential and power-exponential functions:
y = 2ˣ
㏑ y = ㏑ 2ˣ
㏑ y = x ㏑ 2
y' / y = ㏑ 2
y' = y · ㏑ 2
y' = 2ˣ · ㏑ 2
By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
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For each equation, find the center and radius of the circle.
(x-1)²+(y-1)²=1
Answers
The equation of the circle (x - 1)^2 + (y - 1)^2 = 1 has a radius of 1 and a center located at (1 , 1).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x - 1)^2 + (y - 1)^2 = 1, is in standard form, then
h = 1
k = 1
r = 1
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Find the tenth term of each arithmetic sequence. 2,8,14,20, ...........
Answers
The 10th term of the given arithmetic sequence 2,8,14,20, ........... is ( a₁₀ = 56.)
Describe the AP arithmetic progression series?The difference between two mathematical orders is a fixed value in Arithmetic Progression (AP). Arithmetic Sequence is another term for it.
We'd come across a few key words in AP which have been classified as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be viewed in terms of common differences, as illustrated below.
The following is the process for evaluating an AP's n-th term: an = a + (n − 1) × dThe so these is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the sequence given in the question is; 2,8,14,20, ...........
Define the first term as 'a₁' = 2.
Define 'a₂' = 8 is the second term.
Define the third term as 'a₃' = 14.
Evaluate the common difference;
d = a₂ - a₁
Put the values in the obtained equation;
d = 8 - 2 = 6
Now, to evaluate the value of the 10th term imply the formula of nth term.
an = a + (n − 1) × d , n = total number of terms = 10.
Substitute all the values;
a₁₀ = 2 + (10 - 1) × 6
a₁₀ = 2 + 9 × 6
a₁₀ = 2 + 54
a₁₀ = 56.
Therefore, the value of the 10th term is found as a₁₀ = 56.
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3 squared by 6 squared?
Answers
Answer: 1/4
Step-by-step explanation:
3^2 / 6^2 =
(3/6)^2=
(1/2) ^ 2=
1^2 / 2^2 = 1/4
Use the spinner to find following probability. The spinner is spun again if it stops on a line.
P (pointer landing on yellow)
Answers
The probability of the spinner's point landing on yellow is 30.56%.
What exactly would be a pie chart?A pie graph is a type of chart which displays data in the form of a circular graph.
We understand that the total value of the pie is always 100%. It is also understood that a circle will have a circumference of 360°. As a consequence, the total of all data points equals 360°. There appear to be two main pie chart formulas based on these:
To evaluate a proportion of the data set, we just use following formula: (Frequency ÷ Total Frequency) × 100To transform the information to degrees, we should use following formula: (Mentioned Data ÷ Total value of Data) × 360°When a circle is completely rotated, it forms a 360-degree angle in the center.
The overall percentage of all colors is 100%.
Because 360 degrees / 100 percent = 3.6, divide the valuation of yellow by 3.6.
The total percentage of yellow displayed by the spinner's pointer is 110%.
P (probability of landing on yellow) = 110/3.6
P (probability of landing on yellow) = 30.555... = 30.56 (approx.)
As a result, the probability of the pointer landing on the yellow is 30.56%
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12. A 500 N force is applied to a 25 m/s² object. The mass of the object is
A. 12,500 kg
B. 12,500 m/s
C. 20 kg
D. 20 m/s
Answers
Answer:
C is right 20kg
Step-by-step explanation:
bec
ause the formula of force=mass ×acceleration
to find mass= force/acceleration.
Evaluate 4-0.25g + 0.5h when g=10 and h=5
Answers
not really sure though
Find the arithmetic mean a n of the given terms. a n₋₁ = 0.3, a n₊₁ = 1.9
Answers
The arithmetic mean a n of the given terms a n₋₁ = 0.3, a n₊₁ = 1.9 is
a n = 1.6.
What is direct variation?
a n₋₁ = 0.3, a n₊₁ = 1.9
a n = a [tex]n_{+1}[/tex] - a[tex]n_{-1}[/tex]
a n = 1.9 - 0.3
a n = 1.6
Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.
The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.
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Solve for W
5 = 7w + 8w + 2
Answers
What you want to do is isolate W. Add the two W terms together and subtract two to isolate and combine like terms.
w = 5
Step-by-step explanation:
2+(7w)+(8w)=5
(7÷5)+(8÷5)+2
(1.4) (1.6) +2
+1.5
=3+2=5
Write –0.67 as a fraction.
Answers
Answer:
- [tex]\frac{67}{100}[/tex]
Step-by-step explanation:
there's a negative sign so the our fraction will also have a negative sign
notice each number and its position. 0 is at the ones position. 6 is at the tenths position. 7 is at the hundredths position. 1, 10, 100, 100, etc.
The denominator of a fraction will be 100, because that is the last position of this decimal.
the numerator is just the number value itself.
in total it is
- [tex]\frac{67}{100}[/tex]
Answer:
[tex] - \frac{67}{100} [/tex]
is this what you asked for?
Can please help me with this question
Answers
The possible coordinates of point G on the number line is -15 and 7.
How to find the coordinates on a number line?On the number line, point E has the coordinates of - 4, and EG = 11 .
The possible coordinates of point G are as follows:
A number line is a horizontal straight line with numbers placed at equal distances from each other along that line.
Negative numbers are on the left side while the positive numbers are on the right side.
Therefore, the possible coordinates of G is when we go left or right side of E on the number line.
Hence,
Let's go left E to G on the number line
-4 - 11 = -15Let's go right E to G on the number line
-4 + 11 = 7Therefore, the possible coordinates of point G on the number line is -15 and 7.
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Identify the number as prime, composite or neither. If the number is composite, write it as the product of prime factors. 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The number is composite. Its prime factors written as a product are ( )
B. The number is prime.
C. The number is neither prime nor composite.
Answers
The correct option regarding number 1 is given by:
C. The number is neither prime nor composite.
What are prime numbers?Prime numbers are numbers that have only two factors, that are 1 and itself. Examples of prime numbers are 2, 3, 5, 7, and so on...
Number 1 has only one factor, itself, hence for this reason it is neither prime(two factors are needed) nor composite, as it cannot be written as a product of two numbers both different than 1, hence option c is correct.
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Alec's car payment is $316 each month.
How much do his car payments
year?
Answers
Answer:
$3,792
Step-by-step explanation:
$316 x 12
Which number is divisible by both 2, 5, and 10?
Answers
Answer: A number that ends in 0 is divisible by 2, 5, and 10. 6730 is divisible by 2, 5, and 10, which means that it is in the 2, 5, and 10 times tables.
Step-by-step explanation:
Answer: 6,730
Step-by-step explanation: A number is divisible by 10 if it ends in a 0. The number ends in a 0 and so it is divisible by 10. A number that ends in 0 is divisible by 2, 5 and 10. 6730 is divisible by 2, 5 and 10, which means that it is in the 2, 5 and 10 times table.
ax+ 5x = 10b; solve for x
Answers
Answer:
[tex](a + 5) \times = 10b \\ \times = \frac{10b}{a + 5} [/tex]
x
=
10
b
a
−
5
a
Use the given information to write an equation of the circle.
center (6,4) , through (2,1)
Answers
Using the given information, the equation of the circle with center located at point (6 , 4) and passes through the point (2 , 1) is (x - 6)^2 + (y - 4)^2 = 25.
Using the distance formula, get the radius of the circle by solving for the distance between the center (6 , 4) and the point (2 , 1).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(2 - 6)^2 + (1 - 4)^2
radius= √16 + 9
radius = √25
radius = 5
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (6 , 4)
r = 5
(x - 6)^2 + (y - 4)^2 = 5^2
(x - 6)^2 + (y - 4)^2 = 25
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Rewrite x4y2-6x3y3 using a common factor
Answers
Answer:
[tex]x^4y^2-6x^3y^3 = x^3y^2(x - 6y)[/tex]
Step-by-step explanation:
to pick out common factors, you have to find the highest common denominator. We start by listing units and variables:
we can divide the x^4y^2 by up to x^4 and up to y^2, cannot divide by non-variable numbers
we can divide 6x^3y^3 by up to x^3 and up to y^3, and by 6 if we needed to.
This means that for units, we're not dividing (because we can't simplify x^4y^2 dividing by a bare number.
For x, we can divide both by x^3, because we can divide both by x^3, but cannot divide 6x^3y^3 by x^4 or more.
For y, we can divide both by y^2, because we can divide both by y^2, but cannot divide x^4y^2 by x^3 or more.
We take the x^3y^2 and bring it in front of the brackets.
Disclaimer: when I say "cannot divide" I mean "cannot divide without introducing fractions or negative exponents".
Find the equation for the line parallel to 3x+5y-4=0, with the same x-intercept as 2x-3y-6=0
Answers
Equation of line is 5y = -3x + 9 .
What is equation of line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
3x+5y-4=0
5y = -3x + 4
y = -3/5 x + 4/5
since it is parallel, its slope, m is -3/5
2x-3y-6=0
3y = 2x - 6
y = 2/3x - 2
at x-intercept, y is zero
2 = 2/3x
x = 3
therefore
y = mx + c
0 = (-3/5 * 3 ) + c
c = 9/5
equation is
y = -3/5x + 9/5
5y = -3x + 9
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nancy wants to vacation in austin texas. Hotel A charges $179 per night with a 14% nightly room tax and free parking. Hotel B charges $169 per night with 18% nightly room tax plus a one time $40 parking fee. After how many nights will Hotel B be less expesnsive?
Answers
The number of nights will be 8.62 when the Hotel B charge is less than A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that hotel, A charges $179 per night with a 14% nightly room tax and free parking. Hotel B charges $169 per night with 18% nightly room tax plus a one-time $40 parking fee. The number of the nights will be calculated as below:-
From the given data from the equations:-
A = 179 + ( 0.14 x 179 ) x
A = 204.06x
B = ( 169 + ( 0.18 x 169 )x + 40
B = 199.42x + 40
Equate the two equations:-
204.06x = 199.42x + 40
4.64x = 40
x = 40 / 4.64
x = 8.62 nights
Therefore, the number of nights will be 8.62 when the Hotel B charge is less than A.
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I really don't get this can someone help meh please :d
Answers
Answer:
this is a vertical problem what is on one side is on the other
Step-by-step explanation:
so r is the same as 95
what is the equation for the standard form of the line that has an x-intercept of 3 and a y-intercept of 5
Answers
5x+3y=15 is the equation for the standard form of the line .
What is in slope-intercept form?
Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.We are given two coordinates (3,0) (0,5)
Start by finding slope
y2-y1/x2-x1= 5-0/0-3= -5/3 this is your slope m.
y=mx+c
y= -5/3x+c (but remember standard line is ax+by=c) so we have to switch sides
5/3x + y=5 (remember standard form has no fraction so multiply by 3 on all sides)
5x+3y=15
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What is the sum? Enter your answer as a mixed number in the simplest form.
HELLPPPPPPPPPPP
1/3+ 5 3/4
Answers
Equation: 5•3=15
15/4+1/3
4•3=12. 15•3=45
4•1=4
45/12+4/12= 49/12
Simplest form is 4 1/12
Please help i'm stuck
Answers
Answer:
Decreases two times
Step-by-step explanation:
[tex].[/tex]
Explanation: the cost drops twice.
What is the measure of n?
6
3
n
18
n = [?]√
Answers
In the triangle, The measure of side n is √ 108
What is a Triangle ?It belongs to the basic geometric forms. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a separate triangle and a distinct plane.
Identical sides have the same ratio since all of the triangles in the example are comparable.
Short side/long side:
n/6 = 18/n
n² = 6*18
n² = 108
n = √ 108
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The domain is 0, 1, 2, 3, 4, and 5. What is the range? Select all that apply.
Answers
Considering the numeric values and the range concept, we have that:
The range of the function is given by: {f(0), f(1), f(2), f(3), f(4), f(5)}.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
The range of a function is the set that contains all possible output values for the function. These outputs are the numeric values for the domain of the function, which compose the input values.
For this problem, we have that:
The domain is composed by: 0, 1, 2, 3, 4 and 5.The outputs for the function will be given by: f(0), f(1), f(2), f(3), f(4), f(5).Hence:
The range of the function is given by: {f(0), f(1), f(2), f(3), f(4), f(5)}.
The function is not given, hence this problem was solved speaking in general terms. In your problem, you will mark the numeric values of the function given.
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If x is 6, then 7x =
Answers
Answer:
42
Hope this helps :)
Step-by-step explanation:
1. Substitute x with 6 since x is 6. When a variable is next to a number multiply them. Also, multiply when number is next to parenthesis.
7(6)
2. Solve by multiplying.
7(6) = 42
Check:
42 ÷ 7 = 6 ✓
43.95 divided by 16.2
Answers
Answer:
2.712
Step-by-step explanation:
2.712
Y=44 when x=a^3
Y is inversely proportional to the cube of x
Show us that y=5.5 when x=2a
Answers
Answer:
0.283258167471352[tex]\sqrt[3]{k}[/tex]
Step-by-step explanation:
Based on the given conditions, formulate:
Write the equation of the function:
Substitute and calculate:
Calculate the value of x.
Give your answer as an integer or as a fraction in its simplest form.
Answers
10 x 4.5 = 45
therefore, x = 45cm
Pls pls help whoever gets it right gets a crown
Answers
Answer:
last one is right
Step-by-step explanation:
multiply 8 by X is 8x and 8 multiplied by 8 is 64
Hope it helps
Answer: 8x+64=8x(x+8)
Step-by-step explanation:
8 is a common of 8 so 8x8=64
