Please help me! Due soon!
The quadratic [tex]3x^2+4x-9[/tex] has two real roots. What is the sum of the squares of these roots? Express your answer as a common fraction in lowest terms.
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Answers
Answer:
70/9
Step-by-step explanation:
We have the quadratic:
[tex]3x^2+4x-9[/tex]
So, let’s find the roots of the quadratic. We will set the expression equal to 0:
[tex]3x^2+4x-9=0[/tex]
Testing for factors, we can see that our quadratic isn’t factorable.
So, we can use the Quadratic Formula. The quadratic formula is given by:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case:
[tex]a=3, b=4,\text{ and } c=-9[/tex]
Therefore, by substitution:
[tex]\displaystyle x=\frac{-(4)\pm\sqrt{(4)^2-4(3)(-9)}}{2(3)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{-4\pm\sqrt{124}}{6}[/tex]
Simplify the square root:
[tex]\sqrt{124}=\sqrt{4\cdot31}=2\sqrt{31}[/tex]
Hence:
[tex]\displaystyle x=\frac{-4\pm2\sqrt{31}}{6}[/tex]
Reduce:
[tex]\displaystyle x=\frac{-2\pm\sqrt{31}}{3}[/tex]
So, our roots are:
[tex]\displaystyle x_1=\frac{-2+\sqrt{31}}{3}, x_2=\frac{-2-\sqrt{31}}{3}[/tex]
We want to find the sum of the squares of our two roots. So, let’s square each term:
[tex]\displaystyle (x_1)^2=\Big(\frac{-2+\sqrt{31}}{3}\Big)^2[/tex]
Square. For the numerator, we can use the perfect square trinomial patten where:
[tex](a+b)^2=(a^2+2ab+b^2)[/tex]
Therefore:
[tex]\displaystyle (x_1)^2=\Big(\frac{(-2)^2+2(-2)(\sqrt{31})+(\sqrt{31})^2}{9}\Big)[/tex]
Simplify:
[tex]\displaystyle (x_1)^2=\frac{35-4\sqrt{31}}{9}[/tex]
Similarly, for the second root, we will have:
[tex]\displaystyle (x_2)^2=\Big(\frac{-2-\sqrt{31}}{3}\Big)^2[/tex]
So:
[tex]\displaystyle (x_2)^2=\Big(\frac{(-2)^2+2(-2)(-\sqrt{31})+(-\sqrt{31})^2}{9}\Big)[/tex]
Simplify:
[tex]\displaystyle (x_2)^2=\frac{35+4\sqrt{31}}{9}[/tex]
Therefore, our sum will be:
[tex]\displaystyle (x_1)^2+(x_2)^2\\\\ \begin{aligned} &=\frac{35-4\sqrt{31}}{9}+\frac{35+4\sqrt{31}}{9}\\&=\frac{35-4\sqrt{31}+35+4\sqrt{31}}{9}\\&=\frac{70}{9}\end{aligned}[/tex]
Therefore, our final answer is 70/9.
Related Questions
can someone help answer this?
Answers
9√2 is squared first.
so its 162.
now according to Pythagoras theorem,
x2+x2=162
2x^2= 162
x^2= 162÷2
x^2= 81
x= √81
x=9
in a right angled triangle, (height)^2 + (base)^2 = (hypotenuse)^2
here we have , height as X and base as X too , so; x^2 + x^2 = (9√2)^2
2(X)^2 = 162
x^2 = 162/2
X^2 = 81
X = √81 = 9
Write this percentage as a fraction in its simplest form.
46%
Answers
Answer:
23/50
Step-by-step explanation:
46% is the same as 46/100 that can be simplified to 23/50
The percentage 46% as a fraction in its simplest form is 23/50.
The given fraction is 46%.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
The percentage can be written in fraction by dividing the number by 100.
Here, 46% = 46/100
= 23/50
Therefore, the percentage 46% as a fraction in its simplest form is 23/50.
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brainly.com/question/24159063.
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In the expression 5+9x, which is the constant?
Answers
Answer:
The constant in this expression is 5 (btw, a constant is a number on its own)
I need the answers please !
Answers
Answer:
m<5 = 133°
m<8 = 47°
Step-by-step explanation:
if <2 = 47°, and <5 is supplementary to <2, that means that together they both have to equal 180°. So, to get the measure of <5, you need to do 180 - 47 to get <5 = 133°.
Now, <5 (133°) is supplementary to <8, so they both have to equal 180° together. So, you must do 180 - 133 to get <8 = 47°. Or, another way to get <8 is to notice that <2 and <8 are alternate interior angles, which means they equal the same amount. So if <2 = 47°, then so does <8.
guys Im getting a tattoo I'm 13 tho..but should I get butterflies or hearts? let me know assasp
Answers
A photo that measure 5 inches in length by 7 inches in width is enlarged to 7.5 inches in length. What is the width?
Answers
Answer:
10.5
Step-by-step explanation:
You can use ratios to solve this problem.
The original dimensions of the photo is
5 in. by 7 in.
This can be written as:
5:7
And the next is 7.5:?
Then you can use ratios to solve this.
5:7=
7.5:?
5*1.5=7.5 so you can multiply the other side by the same thing. 7*1.5=10.5
The width is 10.5 inches.
Add the equation u-v/8v + 6u-3v/8v
Answers
Answer:
7u-4v/8
Step-by-step explanation:
u+6u=7u
-v+(-3v)=-v-3v=-4v
7u-4u/8
9x+16y=5 solve for y
Answers
Answer:
its y=-4+9x/4
what polynomial function has the zeros -3,1,5
Answers
Answer:
x³ - 3 x² - 13 x + 15 = 0
Step-by-step explanation:
Basically you can create three factors like this:
(x+3)(x-1)(x-5)=0
That will each represent one zero.
Work it out and you get x³ - 3 x² - 13 x + 15 = 0
If I make $1,000 per minute how much time will it take to make $1,000,000?
Answers
Answer:
it would take 1,000 minutes
Step-by-step explanation:
1,000,000/1,000=1,000
Answer: I think it’ll take 1,000 minutes
Step-by-step explanation:
If you multiply 1,000 and 1,000 it’ll equal 1 million.
Hoped this helps.
John walks m miles each week. Marie’s distance can be found by using the expression : 3m + ½
If John walks 7 miles in one week, how many miles does Marie walk?
Answers
Answer:
21.5 Miles or 21 ½ Miles
Step-by-step explanation:
Plug in 7 as m to 3m + ½.
Then, I get 3(7) + ½.
That concludes to 21 + ½
Add the ".5" or "½" at the end
So, answer is you get is 21.5 of 21 ½
Please help me on these two
Answers
Answer:
1. A
2. A
Step-by-step explanation:
Im pretty sure that is correct
Which of the following equations is equivalent to 2(3x - 1) = 3 - (- 2 - x)?
1. 6x - 2 = 1 - 4
2. 6x - 1 = 1 + x
3. 6x - 2 = 5 + x
4. 6x - 1 = 5 - x
Answers
Answer:
It would be 2. 6x - 1 = 1 + x
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
The drawing below shows 3 parking lots that enclose a shopping mall shaped like a right triangle. If Lot A’s perimeter is 40 miles and Lot B’s perimeter is 24 miles, what is the perimeter of Lot C?
Answers
Answer:
40 miles because they are da same size
Step-by-step explanation:
The perimeter of lot C is 46.64 miles
Lot C is a square, hence the perimeter of lot C with a length of each side as a miles is:
Perimeter = 4 * length = 4a
40 = 4a
a = 10 miles
Lot B is a square, hence the perimeter of lot B with a length of each side as b miles is:
Perimeter = 4 * length = 4b
24 = 4b
b = 6 miles
Let c represent the length of lot A,, since a, b, c form a right angle triangle. Using Pythagoras theorem:
c² = a² + b²
c² = 10² + 6²
c² = 136
c = 11.66 miles
Perimeter of lot C = 4 * c = 4 * 11.66 = 46.64 miles
The perimeter of lot C is 46.64 miles
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F(x) = x-10 f(10)=
Can somebody help me
Answers
This is because once the 10 is inputted in the equation as x, you will get:
F(10)= 10 - 10
which results in zero.
1 Fie mulțimea de numere reale: A={5;-3,1(7);-3; 2,8; 213; -49}.
Determinați mulțimea AZ.
Determinați mulțimea A(R-Q).
Ordonați crescător elementele mulțimii A.
Answers
Answer:
j is the answer
Step-by-step explanation:
thats correct
use the multiples method to find Least common denominator , then find the sum or difference , please help me understand dis ill mart brainliest
Answers
Answer:
25/28
Step-by-step explanation:
3/4+1/7
21+4/28
25/28
What’s 3(2y+6c+4) if y=6 and z=1
Answers
Answer:
210
Step-by-step explanation:
HELPpPppPp ASAP I rlly need help I’m timeddddd frrr I will give u a Brainly thing just help and show your workkkk
Answers
Answer:
1
I hope this helps! Do you need help on anything else?
Okay here are some pictures of the work, I can't do fractions on this. :)
Patrice and Arnold went to the bank together and checked their account balances Patrice's balance was - 55 and Arnold's was - 56 . Who has a greater debt? Explain using the concept of absolute value.
Answers
Answer:
Arnold has greater debt because he owes an extra dollar to the bank
Step-by-step explanation:
simplify 8r - 3j + 9j - 2r
Answers
Answer:
6j + 6r :)))))))))))))))))
Answer:
6j + 6r
Step-by-step explanation:
The slope of a line is 1/7 and it passes through the point (21, 14). What is
the equation of the line in point-slope form?*
Answers
Answer: the equation of the line is y=1/7x+11
Baxter runs ¾ the length of the backyard every ½ of a minute. Enter the number of lengths of the backyard Baxter runs per minute.
Answers
Answer:
Baxter runs 3/2 lengths of the backyard per minute.
Step-by-step explanation:
The question is asking how many times Baxter runs the length of the backyard per minute. We know that he runs 3/4 of the backyard every 1/2 of a minute. This means that he runs 6/4 (simplified to 3/2) per minute.
Evaluate f(x) = 2x +3 for f(4)
Answers
f(x)=2x+3
f(4)= 2*4+3= 8+3=11
Retail Sales: HELP! 15 POINTS AND BRAINLIEST
Suppose you have a $5-off coupon at a fabric store. You buy fabric that costs $7.50 per yard. Write an equation that models the total amount of money y you pay if you buy x yards of fabric. What is the graph of the equation?
Answers
Answer:
7.5x-5 is equation for graph :)
BRAINLIEST PLEASE
Step-by-step explanation:
Which problems can be solved by performing this multiplication? 23×18 Select each correct answer. Sarah mixed 18 ounces of orange juice with 23 ounce of pineapple juice. How many ounces of juice did she have in all? A container held 18 ounces of water. Two-thirds of the water leaked out of the container. How many ounces of water were left in the container? Jordan had 18 coins. Two-thirds of the coins were dimes. How many coins were dimes? Min had 18 quarters. He used 23 of the quarters to play arcade games. How many quarters did Min use?
Answers
Answer:
Jordan had 18 coins. Two-thirds of the coins were dimes. How many coins were dimes?
Min had 18 quarters. He used 2/3 of the quarters to play arcade games. How many quarters did Min use?
Step-by-step explanation:
2/3 × 18
Checking all options
Sarah mixed 18 ounces of orange juice with 23 ounce of pineapple juice. How many ounces of juice did she have in all?
Ounces of orange juice = 18
Ounces of pineapple juice = 23
Total ounces of juice = 18 + 23
= 41 ounces
A container held 18 ounces of water. Two-thirds of the water leaked out of the container. How many ounces of water were left in the container?
Total water in the container = 18
Water leaked out = 2/3
Ounces of water left = 18 - 2/3(18)
= 18 - 36/3
= 18 - 12
= 6
Jordan had 18 coins. Two-thirds of the coins were dimes. How many coins were dimes?
Total Number of coins = 18
Dimes = 2/3 of 18
Number of dimes = 2/3 × 18
= 36 / 3
= 12
Min had 18 quarters. He used 2/3 of the quarters to play arcade games. How many quarters did Min use?
Total quarters = 18
Quarters used for game = 2/3 × 18
= 2/3 × 18
= 36 / 3
= 12
6z + 10 = -2 How should I solve it? It's from Simple Equations
Answers
Answer: z = -2
Step-by-step explanation:
6z + 10 = -2
add 10 on both sides
6z = -2 -10
6z = - 12
divide 6 on both sides
z = -2
Answer:
z= -2
Step-by-step explanation:
6z+10=-2
-10. -10
6z = -12
÷6. ÷6
z= -2
A 3.0 kg book sits on a very high shelf 4.5 meters above the ground. Calculate the potential energy of the book.
Answers
MASS=3
GRAV=9.8
HEIGHT=4.5
3*9.8*4.5=132.3
POTENTIAL ENERGY= 132.3
Please help and explain process too. Thank you!!
Answers
HElp for brianliest PELASEEE EHELPPPPPP
Answers
Answer:
Perimeter of the given figure is :---
[tex](2n) + (2n) +( n + 5) + (n + 5) + (3n + 3) \\ = 2n + 2n + n + 5 + n + 5 + 3n + 3 \\ = \boxed{9n + 13}✓[/tex]
(9n+13) is the right answer