![X =x + 6x + 5 = 0b= ] B22-4aaC](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/IWQc35fFn5cLddsLCgSGYqD2Bd0VuBjL.jpeg)
Answers
We have the following quadratic equation:
[tex]x^2+6x+5=0[/tex]And we have to use the quadratic equation to solve that equation.
1. To find the solutions, we need to start by using the quadratic equation:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \text{ when }ax^2+bx+c=0 \end{gathered}[/tex]2. Identify a, b, and c from the given quadratic equation:
[tex]\begin{gathered} x^2+6x+5=0 \\ \\ a=1,b=6,c=5 \end{gathered}[/tex]3. Apply the quadratic equation:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-6\pm\sqrt{6^2-4(1)(5)}}{2(1)} \\ \\ \\ \end{gathered}[/tex]4. And now, we can develop it as follows:
[tex]\begin{gathered} x=\frac{-6\pm\sqrt{36-20}}{2} \\ \\ x=\frac{-6\pm\sqrt{16}}{2} \\ \\ x=\frac{-6\pm4}{2} \\ \\ \text{ Therefore:} \\ \\ x=\frac{-6+4}{2}=-\frac{2}{2}=-1 \\ \\ x=-1 \\ \\ x=\frac{-6-4}{2}=\frac{-10}{2}=-5 \\ \\ x=-5 \end{gathered}[/tex]Therefore, we finally have two solutions, x = -1, and x = -5.
Then the first step is given by:
[tex]x=\frac{-6\pm\sqrt{6^2-4(1)(5)}}{2(1)}[/tex]
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Related Questions
What type of linear equation is X +1 equals X +1?
Answers
The given equation is 1-degree linear equation in one variable.
What is linear equation?
A linear equation is one that may be written as a1x1+a2x2+......+anxn in mathematics, where a1, a2,...., an are the coefficients, which are frequently real integers. The coefficients, which may be any expressions as long as they don't contain any of the variables, can be thought of as the equation's parameters. The coefficients a1 to a must not all be 0 in order for the equation to have any sense. An alternative method for creating a linear equation is to equalize a linear polynomial over a field, from which the coefficients are drawn, to zero. The numbers that, when used to replace the unknowns in such an equation, result in the equality, are the solutions.
x+1 = x+1 is a 1-degree linear equation in one variable (x).
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Maximize:
z= 6x +12y
subject to: 4x + 5y ≤20
8x + y ≤ 20
x≥0, y 20
Answers
Answer:
48
Step-by-step explanation:
Given:
[tex]\textsf{Maximize}: \quad z=6x+12y[/tex]
[tex]\begin{aligned}&\textsf{Subject to}: \quad &4x+5y & \leq 20\\&&8x+y &\leq 20\\&&x\geq 0, y&\geq 0\end{aligned}[/tex]
Graph the lines:
[tex]\textsf{Draw the line } \;\;4x+5y=20 \;\;\textsf{and shade under the line}.[/tex]
[tex]\textsf{Draw the line } \;\;8x+y=20 \;\;\textsf{and shade under the line}.[/tex]
[tex]\textsf{Draw the line } \;\;x=0\;\;\textsf{and shade above the line}.[/tex]
[tex]\textsf{Draw the line } \;\;y=0\;\;\textsf{and shade above (to the right of) the line}.[/tex]
Therefore, the feasible region is bounded by the corner points:
A = (0, 0)B = (0, 4)C = (⁵/₂, 0)D = (²⁰/₉, ²⁰/₉)Determine the value of z at the corner points by substituting the x and y values of the points into the equation for z:
[tex]\textsf{Value of $z$ at $A(0,0)$}: \quad 6(0)+12(0)=0[/tex]
[tex]\textsf{Value of $z$ at $B(0,4)$}: \quad 6(0)+12(4)=48[/tex]
[tex]\textsf{Value of $z$ at $C\left(\dfrac{5}{2},0\right)$}: \quad 6\left(\dfrac{5}{2}\right)+12(0)=15[/tex]
[tex]\textsf{Value of $z$ at $D\left(\dfrac{20}{9},\dfrac{20}{9}\right)$}: \quad 6\left(\dfrac{20}{9}\right)+12\left(\dfrac{20}{9}\right)=40[/tex]
Hence, the maximum value of z is 48 at B(0, 4).
Is any real number exactly 2 more than its cube?
Answers
Answer: Yes
Step-by-step explanation: The real number, which most exceeds its cube, is A 21
If Rebekah can run 6 miles every 60 minutes, how
many miles can she run in 50 minutes?
Answers
Answer:
5 miles in 50 minutes
50 divided by 10 = 5.
So the answer is 5 miles
[tex] \rm \int_{0}^{1} \sqrt{ \frac{2 - {x}^{2} }{1 - {x}^{2} } } dx \\ [/tex]
Answers
Substitute [tex]x=\sin(t)[/tex] and [tex]dx=\cos(t)\,dt[/tex], and recall the definition of the elliptic integral of the second kind,
[tex]\displaystyle E(k) = \int_0^{\pi/2} \sqrt{1 - k^2 \sin^2(\theta)} \, d\theta[/tex]
Then the integral has a value of
[tex]\displaystyle \int_0^1 \sqrt{\frac{2-x^2}{1-x^2}} \, dx = \int_0^{\pi/2} \sqrt{2-\sin^2(t)} \, dt \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \sqrt2 \int_0^{\pi/2} \sqrt{1 - \frac12 \sin^2(t)} \, dt \\\\ ~~~~~~~~~~~~~~~~~~~~~= \boxed{\sqrt2 E\left(\frac1{\sqrt2}\right)}[/tex]
Answer for this question
Answers
Answer:
Proofs provided below
Step-by-step explanation:
[tex]\bold {\text{Prove } (a + b)^2 = a^2 + 2ab + b^2}}[/tex]
[tex]\\\\\implies (a + b)^2 = (a+b) \times (a+b)\\\\\implies (a + b)^2 = a \times (a+b) +b \times (a+b)\\\\\implies (a + b)^2 = a \times a + a \times b + b \times a + b \times b\\\\\implies (a + b)^2 = a^2+ab+ba+b^2\\\\\implies (a + b)^2 = a^2+ab+ab+b^2 \;\;\;\;\text{ since ab = ba}\\\\\implies (a+b)^2 = a^2+2ab+b^2\\\\[/tex]
[tex]\bold{\text{Prove } a^2-b^2 \,=\, (a+b)(a-b)\\\\}[/tex]
1. Add and subtract ab to LHS
[tex]\implies a^2-b^2 = a^2-b^2-ab+ab\\\\\implies a^2-b^2 = a^2-ab+ab-b^2\\\\[/tex]
2. Factorize the above expression
[tex]\implies a^2-b^2 = a(a-b)+b(a-b)\\\\\implies a^2-b^2 = (a-b)(a+b) \;\;\;\; \text{since (a-b) is a common factor in RHS }[/tex]
∴ (a² - b²) = (a - b) (a + b)
[tex]\bold{\text{Prove $\dfrac{\sqrt{3}+1}{\sqrt{3}-1}$= $2+\sqrt{\ensuremath{3}}$}}\\[/tex]
[tex]\text{1. Multiply LHS by $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$}\\\\\implies $\dfrac{\sqrt{\text{}3}+1}{\sqrt{3}-1}$ \times $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$ \\\\[/tex]
[tex]\implies \dfrac{ (\sqrt{3} + 1)(\sqrt{3}-1) }{(\sqrt{3} - 1)(\sqrt{3}-1) }\\\\[/tex]
Numerator is
[tex](\sqrt{3} + 1)(\sqrt{3}-1) = (\sqrt{3})^2 - 1^2 = 3 - 1 = 2\\\\[/tex]
Denominator is
[tex](\sqrt{3}-1)^2 = (\sqrt{3})^2 - 2\cdot \sqrt{3} \;\cdot 1 + (-1)^2\\\\= 3 - 2 \sqrt{3} + 1\\\\= 4 - 2 \sqrt{3}\\\\[/tex]
So LHS becomes
[tex]\dfrac{2}{4 - 2\sqrt{3}} \\\\[/tex]
Dividing numerator and denominator by 2 yields
[tex]\dfrac{2}{4 - 2\sqrt{3}} = \dfrac {1}{2 - \sqrt{3}}[/tex]
Multiply numerator and denominator by [tex]{2-\sqrt {3}}[/tex]
[tex]$\dfrac{1\cdot(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3)}}$[/tex]
[tex]=$\dfrac{\ensuremath{2}+\sqrt{3}}{2^{2}-(\sqrt{3)^{2}}}=$$\dfrac{\ensuremath{\ensuremath{2}+\sqrt{3}}}{4-3}=\ensuremath{2}+\sqrt{3}$[/tex]
Hence Proved
I need help i dont understand this
Answers
Answer:
oh god what da heck is this math :')
Step-by-step explanation:
If a new truck is valued at $19,700, what will its value be in 1 year if it depreciates 14.4 % each year?
Answers
depreciated value of truck after 1year is $16863.2
WHAT IS PERCENTAGE ?% is a relative number that is used to represent hundredths of any quantity. Since one percent (1%) equals one tenth of something, 100 percent denotes the entire amount, and 200 percent denotes twice the amount mentioned.
CALCULATIONnew truck valued depreciates 14.4% then
if old truck value be 100 % , depreciated value will be 85.6 %
so depreciated value will be = 19700* 85.6 /100
= $16863.2
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Umm.. Could someone answer this question pls...?
Find the value of v if 4(2v-1)=28
Answers
Answer:
v = 4
Step-by-step explanation:
4(2v - 1) = 28
4(2v - 1)/4 = 28/4
2v - 1 = 7
2v - 1 + 1 = 7 + 1
2v = 8
2v/2 = 8/2
v = 4
f(x) = -4/3 (-x+5)^3 +12
Answers
X Y
3 1.333
4 10.667
5 12
6 13.333
8 48
n(x) = -1 -1/3x + 1 2/3 given x = -2, 0, 5
Answers
The solution to the equations are n(-2) = 4/3, n(0) = 2/3 and n(5) = -1
How to solve the equation using the replacement sets?The equation of the function is given as:
n(x) = -1 -1/3x + 1 2/3
The replacement set is given as
x = -2, 0, 5
So, we replace the variables using the elements in the replacement set
When x = -2, we have
n(-2) = -1 -1/3 x -2 + 1 2/3
Evaluate the equation
So, we have the following equation
n(-2) = 4/3
When x = 0, we have
n(0) = -1 -1/3 x 0 + 1 2/3
Evaluate the equation
So, we have the following equation
n(0) = 2/3
When x = 5, we have
n(5) = -1 -1/3 x 5 + 1 2/3
Evaluate the equation
So, we have the following equation
n(5) = -1
Hence, the values of the functions are 4/3, 2/3 and -1
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Is 6c + 5 an odd integer?
Answers
Yes, because 6 c+5=2(3 c+2)+1 and 3 c+2 is an integer. Option A
This is further explained below.
What is Integer?Generally, A natural number that is either positive or negative expressed as an integer, or the number zero itself are all examples of integers.
The additive inverses of the positive numbers that they relate to are represented by the negative numbers.
In conclusion, Because 6c+5=2(3c+2)+1 and 3c+2 is an integer, the answer to this question is yes.
is correct, Integer
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CQ
[tex](b) Is\ $6 c+5$ \an \odd \integer?\\\\Yes, because $6 c+5=2(3 c+2)+1$ and $3 c+2$ is \ an \ integer.\\\\Yes, because $6 c+5=2(3 c+2)$ and $3 c+2$ is \ an integer.\\\\No, because $6 c+5=2(3 c+2)+1$ and $3 c+2$ is an integer.\\\\No, because $6 c+5=2(3 c+2)$ and $3 c+2$ is an integer.[/tex]
Write an augmented matrix for the following system of equations and give its size.- 8x + 3y = 1 4x - 7y = 4What is the augmented matrix?
Answers
SOLUTION:
The equation is;
[tex]\begin{gathered} -8x+3y=1 \\ \text{ }4x-7y=4 \end{gathered}[/tex]Writing in matrix form, we have;
[tex]\begin{bmatrix}{-8} & {3} \\ {4} & {-7}\end{bmatrix}\begin{bmatrix}{x} & {} \\ {y} & {}\end{bmatrix}=\begin{bmatrix}{1} & {} \\ {4} & {}\end{bmatrix}[/tex]The augmented matrix is thus;
[tex]\begin{bmatrix}{-8} & {3} & |{\text{ }1} \\ {4} & {-7} & |{\text{ }4} \\ {} & {} & \end{bmatrix}[/tex]A forest fire leaves behind an area of grass burned in an expanding circular
pattern. If the radius of the circle of burning grass is increasing with time
according to the formula r(t) = 2t + 1, express the area burned as a function of
time.
Answers
The function of the area of the forest in terms of time is A(t) = π(2t + 1)²
How to determine the area function?The given parameters are
Radius function, r(t) = 2t + 1
From the question, we understand that:
The pattern is circular
The area of a circle is
A = πr²
Express as a function
A(r) = πr²
Substitute r(t) = 2t + 1
A(t) = π(2t + 1)²
Hence, the area function in terms of time is A(t) = π(2t + 1)²
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The carnival spinner shown below is divided into equal sections. On every spin, each outcome is equally likely.
If the spinner lands on a number less than 10 on its next spin, what is the probability that it is a multiple of 4?
a. 1/5
b. 2/9
c. 1/4
d. 1/3
Answers
Answer:
2/9
Step-by-step explanation:
The possibilities that satisfy the condition are 4 and 8.
This is 2 numbers out of the possible 9, so the probability is 2/9.
Please help I’ll mark you as brainliest if correct!!
Answers
Answer:
a = 22, b = 6, c = 14, d = 8
Step-by-step explanation:
sum the elements in the leading diagonal , that is
7 + 15 + 23 = 45
then all other rows and columns and the other diagonal total 45
top row
7 + a + 16 = 45
23 + a = 45 ( subtract 23 from both sides )
a = 22
middle row
24 + 15 + b = 45
39 + b = 45 ( subtract 39 from both sides )
b = 6
left column
7 + 24 + c = 45
31 + c = 45 ( subtract 31 from both sides )
c = 14
bottom row
c + d + 23 = 45 , that is
14 + d + 23 = 45
37 + d = 45 ( subtract 37 from both sides )
d = 8
A dolphin swims at a depth of 13.5 meters below sea level while a seagull flies 10 meters above sea level. How far apart are they? Write and evaluate an expression to answer this question.
Answers
10-(-13.5)= 23.5
Find the area of the figure. 16cm 9cm
area: cm2
Answers
The area of the figure is 144 square centimeters
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the area of the shape?The given parameters are
Shape = parallelogram
Base = 9 cm
Height = 16 cm
The area of a parallelogram shape is
Area = Base * Height
So, we have
Area = 9 * 16
Evaluate the expression
Area = 144
Hence, the area is 144 square centimeters
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Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24.
Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.
They set up the situation with the equation below, where x is the number of pairs of pants.
Is there a situation in which they pay the same amount for their purchases?
Which statements are true? Select all that apply.
17.95x + 24 = 18.95x + 18
There are no solutions to the equation.
There is one solution to the equation.
There are infinitely many solutions to the equation.
There is never a situation in which both girls will pay the same amount for their purchase.
The girls will both pay the same if they buy six pairs of pants and one sweater.
The girls will pay the same amount for any number of pants and one sweater.
Answers
Considering the definition of an equation and the way to solve it, the girls will both pay the same if they buy six pairs of pants and one sweater.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the number of pairs of pants, you know that:
Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24.Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.The equation in this case is:
17.95x + 24 = 18.95x + 18
Solving:
24 -18= 18.95x - 17-95x
6= x
Finally, this means that Kelsey and Jeana pay the same if they buy six pairs of pants and one sweater.
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A z-score less than -2 or greater than 2 is considered unusual in a normal curve. Assuming that the data collected form normal distributions, what would data that is outside the [-2,2] range mean?
Answers
The data points from the set of collected that are outside the [-2, 2] range means that the data is an outlier or unusual data
What is a z–score?The z–score also known as standard score is the number of standard deviation a score is differs from the mean or average score
The z–score is given by the formula;
[tex]Z = \frac{x - \mu}{ \sigma} [/tex]
The Z–Score is therefore, the number of standard deviations, a data point, x is far from the mean, [tex] \mu [/tex]
The standard deviation, [tex] \sigma [/tex], is given by the formula;
[tex] \sigma = \sqrt{ \frac{ \sum {( x_{i} - \mu)}^{2} }{N} } [/tex]
As the value of [tex] \sigma [/tex] increases, the variability increases, and the Z–Score decreases, such that a Z–Score of less than -2 or greater than 2 are unusual.
From the z–score calculator, the probability that a data point has a z–score of less than -2 or more than 2 is 0.02275
Such a data point can be taken as an outlier
Therefore, data that is outside the [-2, 2] range is an unusual (outlier) data
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How did the capture of the forts at Vincennes, Kaskaskia and Cahokia help end the war? A) It helped the Americans control the Ohio Valley. B) It helped the Americans control the Appalachian Mountains. C) It helped the Americans control the Mississippi Delta. D) It helped the Americans control Virginia.
Answers
The capture of the forts at Vincennes, Kaskaskia and Cahokia help end the war because it helped the Americans control the Appalachian Mountains.
What was the Siege of Fort Vincennes?It was the War frontier battle that was fought in present-day Vincennes in which the Indiana won by the militia led by George Rogers Clark over a British garrison led by Henry Hamilton.
What was the Siege of Fort Kaskaskia?The battle happened on 1778 where George Rogers Clark & his men reached Kaskaskia, seized it from the British men and bringing the colonies' battle for independence to the western edge of British territory in North America.
What was the Siege of Fort Cahokia?It was one of the battle that happened in the West as the leader of the secret expeditionary forces captured Kaskaskia, Cahokia and Vincennes in 1778 to 1779.
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Kira and her mom want to make matching pairs of polka-dotted pajama pants. So, they go to the craft store to pick out fabric. Kira needs 4 feet of fabric for her pajamas, and her mom needs 6 feet of fabric. But, the store only sells fabric by the yard. If they buy 4 yards of fabric, how many feet will be left over?
Answers
Answer:
2
Step-by-step explanation:
One yard = 3 feet
4+6 =10
4 times 3 is 12
12 - 10 = 2
There are 16 boys and 12 girls in the running club. What is the ratio of girls to boys?
3:4
16:12
4:3
12:16
Answers
Answer:
4:3
Step-by-step explanation:
it will be 16:12 and when you divide both by 3 it will be 4:3
Which of the following expressions illustrates how you can use the
associative property of addition to solve 13+6.2+5.8 more simply?
a. 13+5.8+6.2
b. (13+6.2)+5.8
c. 13+(6.2+5.8)
d. (13+6.2)+(13+5.8)
Answers
Answer:
c.
Step-by-step explanation:
13+6.2+5.8
= 13+(6.2+5.8)
- the sum in the parentheses is easy to calculate (it = 12).
Find the measure of the angle indicated. Round to the nearest tenth. Make sure that your calculator mode is degrees
Answers
Answer:
The correct answer is c, 24.2°.
Step-by-step explanation:
[tex] { \tan}^{ - 1} ( \frac{7.2}{16}) = 24.2 [/tex]
Find the value of x.
Answers
step by step
Hope this helps
Macy's offers a shirt at the price $300. Then one week later, they offer the shirt at 25% off. The shirt still doesn't sell, so after another week, Macy's reduces its new price by an additional 40% off. How much does the shirt cost now?
Answers
The new cost of the shirt is $135
The new cost of the shirt can be calculated as follows ?Macy's offer a shirt at the cost of $300
One week later, they offer 25% off
25/100 × 300
0.25 × 300
= 75
300-75
= 225
The next week it was reduced by an additional 40% off
40/100 × 225
= 0.4 × 225
= 90
225-90
= 135
Hence Macy's new shirt costs $135
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Find the first 5 terms of the sequence given the nth term.
1. an=2n^2+5n-10
2. an=3n+4/n^2+5
Answers
Part 1: The first five terms of the sequence are -1, 16, 69, 266, 1039
Part 2: The first five terms of the sequence are 12, 12, 130/9, 69/4, 126
Part 1:
For finding the first five terms we will substitute values in n from 1,2,3,4 and 5
an = 2n^2 + 5n-10
a1 = 2(1)^2 + 5(1)-10
=4+5-10 = -1
So, the first term is -1
a2 = 2(2)^2+5(2)-10
= 16+10-10 =16
The second term is 16
a3 = 2(3)^2+5(3)-10
=64+15-10
=69
The third term is 69
a4 = 2(4)^2+5(4)-10
=256+20-10
=266
The fourth term is 266
a5 = 2(5)^2+5(5)-10
= 1024+25-10
= 1039
The fifth term is 1039
Part 2:
an = 3n+4/n^2+5
a1 = 3(1)+4/1^2+5
= 3+4+5
= 12
The first term is 12
a2 = 3(2)+4/2^2+5
= 6+1+5
= 12
The second term is 12
a3 = 3(3)+4/3^2+5
= 9+4/9+5
= 81+4+45/9
=130/9
The third term is 130/9
a4 = 3(4)+4/4^2+5
= 12+4/16+5
=17+1/4
=69/4
The fourth term is 69/4
a5 = 3(5)+4/5^2+5
= 15+4/25+5
=20+4/25
=504/4
= 126
The fifth term is 126
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whats the explicit equation for r=3; f ( 1 ) = 1
Answers
The geometric sequence has an explicit equation of f(n) = 3^(n - 1)
How to determine the explicit equation of the function?The given parameters are
r = 3
f(1) = 1
The above means that we have the following parameters:
Type of sequence: Geometric sequenceFirst term: f(1) = 1Common ratio: r = 3The explicit equation of the geometric sequence is represented as
f(n) = f(1) * r^(n - 1)
Substitute the known values in the above equation
So, we have the following equation
f(n) = 1 * 3^(n - 1)
Evaluate the products
So, we have the following equation
f(n) = 3^(n - 1)
Hence, the explicit equation of the function is f(n) = 3^(n - 1)
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Write an equation of the line through the points (2,1) and (1,4). Write the equation in slope-intercept form.
The equation of the line through the points (2,1) and (1.4) is
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
Answers
The equation of line in slope-intercept form is found as y = -3x + 7.
What is meant by slope-intercept form?The slope-intercept part of a line is a method for writing a line's equation so that the slope and y-intercept are easily recognizable. The slope of the line is its steepness, as well as the y-intercept is where the line intersects the y-axis.For the given question;
The two passing point of the line are;
(x1, y1) = (2,1)
(x2, y2) = (1,4)
Slope = m = (y2 - y1)/(x2 - x1)
Put the values.
m = (4 - 1)/(1 - 2)
m = -3
Then, the equation of the line in slope intercept form is found using two point equation.
y - y1 = m(x - x1)
y - 1 = -3(x - 2)
Simplifying,
y = -3x + 7
-3 is the slope and 7 is the y intercept.
Thus, the equation of line in slope-intercept form is found as y = -3x + 7.
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