Answer:
1. α²+β² = 25/36
2. 1/α+1/β = 1/2
Step-by-step explanation:
Formula :
Consider the quadratic equation ax² + bx + c = 0
Where x₁ and x₂ are the zeros of the equation.
Then
[tex]x_{1}+x_{2}=-\frac{b}{a} \\x_{1}\times x_{2}=\frac{c}{a}[/tex]
……………………………………
α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2
Then
[tex]\alpha +\beta =-\frac{1}{6}[/tex]
[tex]\alpha \times \beta =-\frac{1}{3}[/tex]
……………………
[tex]\alpha^{2} +\beta^{2} =\left( \alpha +\beta \right)^{2} -2\alpha \beta[/tex]
[tex]=\alpha^{2} +\beta^{2} =\left( -\frac{1}{6} \right)^{2} -2\times(-\frac{1}{3} )[/tex]
[tex]=\frac{25}{36}[/tex]
………………………………
[tex]\frac{1}{\alpha } +\frac{1}{\beta } =\frac{\alpha +\beta }{\alpha \beta }[/tex]
[tex]=\frac{-\frac{1}{6} }{-\frac{1}{3} } =\frac{1}{2}[/tex]
Select the correct answer from each drop-down menu. The product of the polynomials (2ab + b) and (a2 – b2) is . If this product is multiplied by (2a + b), the result is a polynomial with terms. The choices for the terms are (7,8,9,10)
First product
(2ab+b)(a²-b²)a²(2ab+b)-b²(2ab+b)2a³b+a²b-2ab³-b³Second and final product
(2a³b)+a²b-2ab³-b³)(2a+b)2a(2a³b+a²b-2ab³-b³)+b(2a³b)+a²b-2ab³-b³)4a⁴b+2a³b-4a²b³-2ab³+2a³b²+a²b²-2ab⁴-b⁴Answer:
Given polynomials
[tex]2ab+b[/tex][tex]a^2-b^2[/tex]The product of the given polynomials:
[tex]\begin{aligned}(2ab+b)(a^2-b^2) & = 2ab(a^2-b^2)+b(a^2-b^2)\\& = 2a^3b-2ab^3+a^2b-b^3\end{aligned}[/tex]
The product of the given polynomials multiplied by [tex](2a+b)[/tex]:
[tex]\begin{aligned}(2a+b)(2a^3b-2ab^3+a^2b-b^3) & = 2a(2a^3b-2ab^3+a^2b-b^3)+b(2a^3b-2ab^3+a^2b-b^3)\\& = 4a^4b-4a^2b^3+2a^3b-2ab^3+2a^3b^2-2ab^4+a^2b^2-b^4\\& = 4a^4b+2a^3b^2-4a^2b^3-2ab^4+2a^3b+a^2b^2-2ab^3-b^4\end{aligned}[/tex]
Therefore, the resulting polynomial has 8 terms.
Can someone give me the steps to solving this?
Answer:
[tex]\tan \theta = \dfrac{8}{15}[/tex]
Step by step explanation:
[tex]\text{Given that,}\\\\~~~~~~~\sin \theta = \dfrac{8}{17}\\\\\implies \sin^2 \theta = \dfrac{64}{289}\\\\\implies 1-\cos^2 \theta = \dfrac{64}{289}\\\\\implies \cos^2 \theta = 1-\dfrac{64}{289}\\\\\implies \cos^2 \theta = \dfrac{225}{289}\\\\\implies \cos \theta =\pm\sqrt{\dfrac{225}{289}}\\\\\implies \cos \theta = \pm\dfrac{15}{17}[/tex]
[tex]\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = \dfrac{15}{17}\\\\\text{Now,}\\\\\tan \theta = \dfrac{\sin \theta }{\cos \theta}\\\\\\~~~~~~~~=\dfrac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=\dfrac{8}{17} \times \dfrac{17}{15}\\\\\\~~~~~~~=\dfrac{8}{15}[/tex]
what is the slope of y=-9x-8?
The slope of the linear equation, y = -9x - 8 is determined as: -9.
How to Identify the Slope in an Equation?If the equation of a line is given in a slope-intercept form, y = mx + b, the slope value is represented as m.
Thus, given the equation y = -9x - 8, the slope in the linear equation is -9.
Therefore, slope of y = -9x - 8 is: -9.
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What does a negative AH₁ for a molecule mean?
Answer: C
Step-by-step explanation: I know it trust me
help me please!!! i cant figure it out and its driving me insane
Answer:
y<_0
Step-by-step explanation:
The last answer.
Hope this helps! Have a great day :)
Solve 3-212.
OA. x≤-30
OB. xs-18
OC. x≥-30
OD. x2-18
The solution of the inequality 3-x/2≥12 is x≤-18
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is 3-x/2≥12
Three minus x by two greater than or equal to twelve
Subtract 3 from both sides
-x/2≥9
-x≥18
x≤-18
Hence, the solution of the inequality 3-x/2≥12 is x≤-18
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A lines slope is 0, and it’s y intercept is 3. What is it’s equation in slope intercept form?
Answer:
y=3
Step-by-step explanation:
y=mx+b where m = slope and b=y-intercept
slope: 0, y-intercept: 3
y=(0)x + 3
y=3
y=x^2-20x+32
What are the zeros of the function using the quadratic formula
By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.
How to find the zeroes of a second order polynomial
A value of x is a zero of a polynomial if and only if [tex]\sum\limits_{i=0}^{n} c_{i}\cdot x^{i} = 0[/tex], the quadratic formula for second order polynomials of the form a · x² + b · x + c = 0 is presented below:
[tex]x =\frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]
If we know that a = 1, b = -20 and c = 32, then the roots of the second order polynomial are:
[tex]x = \frac{20 \pm \sqrt{(-20)^{2}-4\cdot (1)\cdot (32)}}{2\cdot (1)}[/tex]
[tex]x = 10 \pm 2\sqrt{17}[/tex]
By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.
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solve pls brainliest
Answer:
1/6Step-by-step explanation:
-2/3 * (-1/4) =
2/3 * 1/4 =
2/12 =
1/6
Find the sum.
(12x5 - 3x¹ + 2x - 5) + (8x¹ − 3x³ + 4x + 1)
Answer:
[tex]\left(12x^5-3x^1+2x-5\right)+\left(8x^1-3x^3+4x+1\right)[/tex]
=> Expand
[tex]12x^5-3x^1+2x-5+8x^1-3x^3+4x+1[/tex]
=> simplify and group like terms
[tex]12x^5-3x^3+5x^1+6x-4[/tex]
=> simplify further
[tex]12x^5-3x^3+11x-4[/tex]
Please help its very desperate and if i could get someone to help me on this whole assignment it would be awesome
Write -0.65 as a fraction or mixed number in simplest form. (you may use an improper or a mixed number as your final answer.)
also if someone could help me on this whole assignment my discord is goths#0001
Answer:
-13/20
Step-by-step explanation:
-0.65=-65/100
=13/20
Sebastian swam laps every day in the community swimming pool. He swam an hour each day, 5 days each week, for 12 weeks. In
that time, he swam 1,800 laps. What was his average rate in laps per hour?
Answer:
0.25
Step-by-step explanation:
1,800 laps ÷ 12 weeks = 150 laps
150 laps ÷ 5 days each week = 30 laps per day
30 laps per day ÷ 120 hours per week = 0.25 per hour
A museum groundskeeper is creating a semicircular statuary garden with a diameter of 27 feet. There will be a fence around the garden. The fencing costs $7.75 per linear foot. About how much will the fencing cost altogether? Round to the nearest hundredth. Use 3.14 for π.
The fencing will cost about $
.
To calculate the cost of the fence, we have to find the length of the semi-circle. The cost of fencing the garden would be $328.52 approximately
Circumference of a CircleTo find the length of the fence, we have to calculate the circumference of the semi-circle and divide it by 2
[tex]C = 2\pi r\\l = \frac{c}{2} \\l = \pi r[/tex]
Data;
diameter = 27ft r = diameter/2 = 13.5ft π = 3.14Let's substitute the values and calculate the length of the fence.
[tex]l = \pi r\\l = 3.14 * 13.5\\l = 42.39ft[/tex]
The length of the fence is equal to 42.39ft
The cost of fencing would be
[tex]42.39 * 7.75 = $328.5225[/tex]
The cost of fencing the garden would be $328.52 approximately
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add or subtract the given percent from
71% subtracted from 100% is 29%
Complete questionAdd or subtract the given percent from 100%.
71%
How to solve the expression?The percentage (p) is given as:
p = 71%
When subtracted from 100%, we have:
100% - p
Substitute p = 71%
100% - 71%
71 subtracted from 100 is 29.
So, we have:
100% - 71% = 29%
Hence, 71% subtracted from 100% is 29%
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In a a computer game positive numbers represent earning points and negatiive numbers represents.wich number represents losing more than 500 points
Inequalities help us to compare two unequal expressions. The inequality that represents losing more than 500 points is x<-500.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Given In a computer game positive numbers represent earning points and negative numbers represent losing points. Therefore, the loss of more than 500 points is given by the inequality,
x< -500
Hence, the inequality that represents losing more than 500 points is x<-500.
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A boat travelled 60km downstream in 4 hours and the return trip in 5 hours. What is the
speed of the boat in still water in km/h? Write your answer to the nearest tenth.
Answer:
13.3 km/h
Step-by-step explanation:
getting the neutral is adding both the hours and distance, after adding them you can then dicixe the distance by the time getting your average speed (the upstream is what balances the downstream)
heyyy.... can someone pls help asap.
Rearrange the formula to write r in terms of P and pi.
[tex]p = 2r + \pi \: r[/tex]
Answer:
[tex]r = \dfrac{p}{2 + \pi}[/tex]
Step-by-step explanation:
[tex]~~~~~p = 2r +\pi r\\\\\implies p = r(2 + \pi)\\\\\implies r = \dfrac{p}{2 + \pi}[/tex]
Which inequality is shown
Answer:
The choice A.
[tex]y > \frac{3}{2} x + 2[/tex]
which graph shows the solution to the system of linear inequalities below?
y<-1/3x+1
y ≤ 2x-1
The graph that shows the solution set for the system of inequalities is graph C.
Which is the graph of the system of linear inequalities?
Here we have the system of linear inequalities:
[tex]y < (-1/3)*x + 1\\\\y \geq 2x- 1[/tex]
For the first one, we can see a line with a negative slope, and y is strictly smaller than that. So we will have a dashed line that goes down, and we need to shade the region below that line.
For the second inequality, we can see that y can be equal to or larger than the line, so this time we will use a solid line (because the points on the line are solutions). and we will shade above that line.
Also notice that this time the slope is positive, so this line goes upwards.
With that general description, we conclude that the correct option will be graph C.
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Write an equation in slope-intercept form of the line that contains the point (-2, 2) and has the slope = -5.
Answer:
[tex]y=-5x-8[/tex]
Step-by-step explanation:
Given the following question:
To calculate the slope intercept of a line/point we need to use the formula for slope intercept, substitute, and solve for b.
Formula for slope intercept:
[tex]y=mx+b[/tex]
[tex]m=-5[/tex]
[tex]y=2[/tex]
[tex]x=-2[/tex]
[tex]2=-5(-2)+b[/tex]
Solve for b:
[tex]2=-5(-2)+b[/tex]
[tex]-5(-2)=10[/tex]
[tex]2=10+b[/tex]
[tex]10-10=0[/tex]
[tex]2-10=-8[/tex]
[tex]-8=b[/tex]
[tex]b=-8[/tex]
Substitute for the following:
[tex]y=mx+b[/tex]
[tex]b=-8[/tex]
[tex]m=-5[/tex]
[tex]y=-5x-8[/tex]
Your answer is "y = -5x - 8."
Hope this helps.
what is the answer. please help
Answer:
Exact Form:−2/3
Decimal Form:−0.666…
Step-by-step explanation:
There are 50 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?
There are 43 small dogs signed up in the competition
How to determine the number of small dogs?Represent the small dogs with x and the large dogs with y.
So, we have the following equations
x + y = 50
x = 36 + y
Make y the subject in x = 36 + y
y = x - 36
Substitute y = x - 36 in x + y = 50
x + x - 36 = 50
Evaluate the like terms
2x = 86
Divide both sides by 2
x = 43
Hence, there are 43 small dogs in the competition
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Twice during the assembly, a student is chosen at random to assist with the presentation. after the first student has finished assisting, the student returns to the group and can be chosen a second time. what is the probability that the first student chosen is a senior and the second student chosen is a sophomore?.
Using it's concept, it is found that the probability that the first student chosen is a senior and the second student chosen is a sophomore is given by:
[tex]p = \frac{11}{320}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, we have that there are:
31 juniors, 10 sophomores, 17 juniors, 22 seniors.
Then:
Out of 31 + 10 + 17 + 22 = 80 students, 22 are seniors, hence the probability that the first student is a senior is given by [tex]p_1 = \frac{22}{80} = \frac{11}{40}[/tex].All students can be chosen again, hence the probability that the second student is a sophomore is given by [tex]p_2 = \frac{10}{80} = \frac{1}{8}[/tex].The events are independent, hence the probability of both is given by:
[tex]p = p_1p_2 = \frac{11}{40} \times \frac{1}{8} = \frac{11}{320}[/tex]
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write the exprfession 12-2 in simplest form,
A fish tank is full of fish. There are 3 goldfish, 2 guppies, 6 clownfish, and 2 striped fish. If one of the goldfish dies and you remove it from the tank, what is the new probability of selecting a clownfish?
5/13
1/2
5/12
6/13
Answer:
1/2
Step-by-step explanation:
13 total fish
remove one fish
12 total fish
6 total clown fish
6/12 simplified is 1/2
Christian is driving on a long road trip. He currently has 12 gallons of gas in his car.
Each hour that he drives, his car uses up 1.25 gallons of gas. How much gas would be
in the tank after driving for 6 hours? How much gas would bbe left after t hours?
I need help ASAP pleaseee!!
Answer:
Vertex(1,7)
Vertex form: [tex]f(x)=-2\left(x-1\right)^2+7[/tex]
Step-by-step explanation:
Vertex form equations for x is [tex]v=-\frac{b}{2a}[/tex]
which the vertex here is
[tex]-\frac{4}{2\left(-2\right)}[/tex]
->
x = 1, plugin to find y, y = 7
A group of friends are playing a trivia game. players spin a spinner 2 times to find the 2 categories of trivia questions they will be asked. the spinner has 5 sections. the "music" and "sports" sections are each 1-half the size of the 3 larger sections.
to the nearest percentage, what is the probability that a player will be asked a math question ,begin emphasis,and then,end emphasis, a music question? enter the answer in the box.
The probability that a player will be asked a math question and then a music question is 0.03125
How to determine the probability?The size of the sections are given as:
Music = 0.5
Sport = 0.5
Others = 1
So, the total size is:
Total = 0.5 + 0.5 + 1 + 1 + 1
Evaluate
Total = 4
The probability of asking a math question is:
P(Math) = 1/4 = 0.25
The probability of asking a music question is:
P(Music) = 0.5/4 = 0.125
The required probability is:
P(Math and Music) = P(Math) * P(Music)
This gives
P(Math and Music) = 0.25 * 0.125
Evaluate
P(Math and Music) = 0.03125
Hence, the probability that a player will be asked a math question and then a music question is 0.03125
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Solve for the indicated operations.
1) 2/7 + 1/7 + 1/7
2) 4/8 - 3/10
3) 3.5 + 12.11 + 105.007
4) 1 275.25 − 97.75 431
5) 652.835 − 321.6571
Hello, the answer of each option is given below.
[tex]\frac{2}{7}+\frac{1}{7}+\frac{1}{7}=\frac{4}{7}[/tex][tex]\frac{4}{8}-\frac{3}{10}=\frac{(10.4)-(8.3)}{(8.10)}=\frac{16}{80}=\frac{16/16}{80/16}=\frac{1}{5}[/tex][tex]3.5+12.11+105.007=120.617[/tex]Missed equation that's why we can not solve effectively.[tex]652.835-321.6571=331.1779[/tex]Good luck! These are four-operation-equations. We should calculate by our hand or try to use calculator to get the result. Anyway, If you have any question(s), then feel free to ask in comments!
Which image shows a reflection of Polygon P using line e? Select the correct choice.
Answer:
B.
Step-by-step explanation:
Because the point on the top on the original would still be on top so it is 100% B
Hope This Helped