Answer:
The sum of the two solutions to the given equation is 1/3.
Step-by-step explanation:
Nature of Roots of a Second-Degree Equation
Given a quadratic equation:
[tex]ax^2 + bx + c = 0[/tex]
The roots of the equation are:
[tex]\displaystyle x_1=\frac{-b+ \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\displaystyle x_2=\frac{-b- \sqrt{b^2-4ac}}{2a}[/tex]
The sum of the roots is:
[tex]\displaystyle x_1+x_2=-\frac{b}{a}[/tex]
The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient.
We are given the equation:
[tex]3x^2 - x = 4[/tex]
Rearranging:
[tex]3x^2 - x - 4=0[/tex]
The coefficient b is b=-1, and the leading coefficient is a=3, thus the sum of the roots is:
[tex]\displaystyle x_1+x_2=-\frac{-1}{3}[/tex]
[tex]\displaystyle x_1+x_2=\frac{1}{3}[/tex]
The sum of the two solutions to the given equation is 1/3.
will give BRAINLIEST
Find the area of each circle
. Round to the nearest tenth.
Answer:
13: 312yd squared
14: 907.5 rounded up but not rounded is 907.46
Step-by-step explanation:
this is because the formula is pi*r^2 so you'd
Step by step:
1. 20yd/2= 10 to get the radius for 13
2. substitute r in the formula pi*r^2 for 10 making it pi*10^2
3. multiply 10 by itself, 10*10=100
4. multiply pi by 100, 3.14*100= 314
314yd^2 is the answer for 13
14:
1. 34ft/2=17 to get the radius for 14
2. substitute r on the formula pi*r^2 for 17 making it pi*17^2
3. multiply 17 by itself, 17*17=289
4. multiply pi by 289, 3.14*289=907.46
5. round 907.46 to the nearest tenth, 907.5
907.5ft^2 is your answer
hope this helps :)
Find the slope of each line in the figure.
Slope of p =
Slope of q =
Slope of r =
Slope of m =
Slope of n =
Answer:
slope of p= -7/12
slope of q= -3/6.8
slope of r= -16/6.4
slope of m= 6.2/15.5
slope of n= 6.8/17
Step-by-step explanation:
The slopes of the line are given as 2.5 for p and q and -2.5 for r, m and n respectively.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.
The negative slope indicates the rate of decrease while the positive shows the rate of increase.
The slope of the given lines can be obtained as follows,
(a) In order to find slope of line p,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (-3 - 8)/(0.4 - (-4))
⇒ m = -2.5
(b) In order to find slope of line q,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (13 - 0)/(6.8 - 12)
⇒ m = -2.5
(c) In order to find slope of line r,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (13 - (-3))/(6.8 - 0.4)
⇒ m = 2.5
(d) In order to find slope of line m,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (-15.5 - 0)/(0 - 6.2)
⇒ m = 2.5
(e) In order to find slope of line n,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (-5 - 12)/(- 6.8 - 0)
⇒ m = 2.5
Hence, the slopes of first two lines are 2.5 and of the remaining three are 2.5.
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According to a survey conducted by the Texas Free Press, 125 out of 500 people do not have internet access at their homes. What percent of the people surveyed do have internet access at their homes?
Answer:
Step-by-step explanation:
Take 125 and divide by 500 this equals 0.25 or 25%
Answer:
x=25
Step-by-step explanation:
[tex]\frac{125}{500} *\frac{x}{100}[/tex] this is just a typical percent equation
[tex]12500=500x[/tex] cross multiply
x=25 divide by 500 to get the answer
PLEASE HELP
classify triangles
Answer:
I'm pretty sure its obtuse triangle
Please help if you are good at math!!
Answer:
Y intercept= (0,15)
X intercept= ([tex]\frac{3}{4}[/tex],0) , (5,0)
Vertex= -[tex]\frac{b}{2a}[/tex]
Step-by-step explanation:
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Henry can type 3500 words in 70 minutes. Colin can type 1500 in 30 minutes. Brian can type 2200 words in 40 minutes. Who types at the fastest rate of words per minute?
Given:
Henry can type 3500 words in 70 minutes.
Colin can type 1500 in 30 minutes.
Brian can type 2200 words in 40 minutes.
To find:
The person who types at the fastest rate of words per minute.
Solution:
We know that,
[tex]\text{Rate of words per minute}=\dfrac{\text{Number of words}}{\text{Number of minutes}}[/tex]
Using this formula, we get
[tex]\text{Henry's rate of words per minute}=\dfrac{3500}{70}=50[/tex]
[tex]\text{Colin's rate of words per minute}=\dfrac{1500}{30}=50[/tex]
[tex]\text{Brian's rate of words per minute}=\dfrac{2200}{40}=55[/tex]
Since 55>50, therefore Brian's types at the fastest rate of words per minute.
The resultant of the vectors a = 3i - 2j and b = pi - 2pj is parallel to the vector c = 2i - 3j.
a) Find the value of p
b) Find the resultant of vectors a and b.
Please help me with this question, thank you
Part (a)
The resultant vector is the vector formed by adding the two vectors a and b. So we effectively add the corresponding components.
You can use the parallelogram law as a visual alternative.
Adding a and b leads to
a+b = (3i-2j) + (pi-2pj)
a+b = (3i+pi) + (-2j-2pj)
a+b = (3+p)i - (2+2p)j
Define vector d to be d = a+b so we can use it later below.
Recall that parallel vectors point in the same direction. This means the ratio of their components or coordinates are equal.
We can say the following
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
(3+p)/(2) = (-(2+2p))/(-3)
Let's solve for p
(3+p)/(2) = (-(2+2p))/(-3)
(3+p)/(2) = (2+2p)/3
3(3+p) = 2(2+2p) .... cross multiply
9+3p = 4+4p
4p+4 = 3p+9
4p-3p = 9-4
p = 5
Answer: p = 5========================================================
Part (b)
Since p = 5, from part (a), we can determine vector b
b = pi - 2pj
b = 5i - 2*5j
b = 5i - 10j
Then add vectors a and b to get
a+b = (3i-2j) + (5i - 10j)
a+b = (3i+5i) + (-2j - 10j)
a+b = (3+5)i - (2+10)j
a+b = 8i - 12j
Or we can say
a+b = (3+p)i - (2+2p)j .... from part (a)
a+b = (3+5)i - (2+2*5)j ... plugging in p = 5
a+b = 8i - 12j
Note the ratio of the components of vector d and vector c are such
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
8/2 = -12/(-3)
4 = 4
This helps confirm the answer
You could also graph the vectors c = 2i - 3j and d = 8i - 12j to note the two lines produce the same slope -3/2. We can see that -12/8 = -3/2. Lines of the same slope are parallel lines
Answer: 8i - 12ja.
The value of p is 5
Since vector a = 3i - 2j and vector b = pi - 2pj, the resultant of vectors a and b is R = a + b
= 3i - 2j + pi - 2pj
= (3 + p)i - 2(1 + p)j
Since R is aparallel to vector c = 2i - 3j, it implies that the cross product of R and c is zero.
The cross product of two vectors a and b is a × b = absinФ where a and b are the magnitudes of a and b and Ф is the angle between them.
So, R × c = [(3 + p)i - 2(1 + p)j] × [2i - 3j]
= (3 + p)i × 2i + (3 + p)i × (-3j) + (-2(1 + p)]j × 2i + (-2(1 + p)]j×(-3j)
= 0 - 3(3 + p)k - 4(1 + p)(-k) + 0
= -3(3 + p)k + 4(1 + p)k
= [-3(3 + p) + 4(1 + p)]k
= [-9 - 3p + 4 + 4p)]k
= [-9 + 4 - 3p + 4p)]k
= [-5 + p]k
[-5 + p]k = RcsinФ.
Since R and c are parallel, Ф = 0°
So, Rcsin0° = Rc × 0 = 0
So, [-5 + p]k = 0
-5 + p = 0
p = 5
The value of p is 5
b.
The resultant of vectors a and b is R = 8i - 12j
Since p = 5 and the resultant of vectors a and b is R = (3 + p)i - 2(1 + p)j
Substituting the value of p = 5 into r, we have
R = (3 + p)i - 2(1 + p)j
R = (3 + 5)i - 2(1 + 5)j
R = 8i - 2(6)j
R = 8i - 12j
So, the resultant of vectors a and b is R = 8i - 12j
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What error did Tracy make? She used AG = 2EG, but the correct statement is 2AG = GE. She found that x = 4, but the correct value for x is 2. She used GF = 2BG, but the correct statement is BG = 2GF. She found that GF = 64, but the correct value of GF is 8.
Answer:
C. She used GF = 2BG, but the correct statement is BG = 2GF.
Step-by-step explanation:
credits to the other person!
Answer:
C.
Step-by-step explanation:
Edge 2021
help meee will mark brainliest
Answer:
I believe it is B -4/5 I am sorry if I am wrong. If I am right hope this helps and please mark brainlist.
45a^3b^4+36a^2b^5 ÷ 9a^2b^4
3X +17+ 5X equals 7X +10
Answer:
I think the answer is x= -7.
a) Describe the congruence shortcut (postulate/theorem) that could be used to prove that ΔABC≅ΔDEF
b) Explain which parts are congruent in this triangle that applies to the postulate that you chose (naming order matters).(HW)
Answer:
A. By the Side-Side-Side (SSS) Congruence Theorem, ΔABC ≅ ΔDEF.
B. [tex] \overline{AB} \cong \overline{DE} [/tex]
[tex] \overline{BC} \cong \overline{EF} [/tex]
[tex] \overline{AC} \cong \overline{DF} [/tex]
Step-by-step explanation:
a. From the diagram given, it shows that all three sides of ∆ABC are congruent to all the three corresponding sides of ∆DEF.
Therefore, by the Side-Side-Side (SSS) Congruence Theorem, ΔABC ≅ ΔDEF.
b. The sides that are congruent in the ∆s given that applies to the SSS Congruence Theorem are:
[tex] \overline{AB} \cong \overline{DE} [/tex]
[tex] \overline{BC} \cong \overline{EF} [/tex]
[tex] \overline{AC} \cong \overline{DF} [/tex]
[(9 - 6)² - 3 × 5] 20 =
Answer:
the answer is -120
Step-by-step explanation:
trust :)
If 40 percent is 240 what is 25 percent
Answer:
150
Step-by-step explanation:
maybe it could be like this
0.40x = 240
we could get x = 600
then 0.25x = 600 × 0.25 = 150
HELPPP PWEASEEEEEEEEEEEE
8 in. 8 in. 8 in Find the area of the figure above, [?] in
Answer:
96
Step-by-step explanation:
Total area = area of cube + area of triangle
A = 8² + [tex]\frac{8*8}{2}[/tex] = 64 + 32 = 96 in²
Answer:
96 square feet
to find the area of a triangle the formula is
A=1/2×b×h
8×8=64
1/2×8×8=32
32+64= 96
question in pic. please help!
Answer:
Arranging from longest (at top) to shortest (at bottom)
DF
EF
DE
Step-by-step explanation:
We need to place the sides of triangle DE, DF and EF from longest to shortest.
The triangle has longest side that is opposite to the largest angle
We know two angles < E= 61° , <F= 59° we need to find <D
Sum of angles of triangle = 180°
So, 61°+59°+<D=180°
120°+<D=180°
<D=180°-120°
<D=60°
So, the largest angle is <E= 61°
The longest side must be opposite to <E so, the side is DF
The second largest angle is <D=60° so, second side will be EF
The smallest angle is <F=59° so, third (shortest) side will be DE
Arranging from longest (at top) to shortest (at bottom)
DF
EF
DE
Factoring Polynomials Completely Step by step
Answer:
x(x-8)(x+8)
Step-by-step explanation:
it ends with a negative 64 and the only one that also end with that would be C because -8×8 = 64
PLEASE HELP ITS EASY MATH
Workers install 600 chairs at a constant rate. After 4 days, the workers still have to install 360 chairs. How much time does it take to install the chairs from start to finish?
Answer:
10
Step-by-step explanation:
Acc to question, the workers have installed 240 chairs in 4 days which equals 60 chairs in 1 day.
So the will require 600 /60 =10 days from the start.
Felicia earns $800 a month. The table shows her monthly budget.
Monthly Budget
Expense Amount of Money
College savings $200
Car payment $275
Cell phone $125
Clothes $50
Food $100
Other $50
Which statement is supported by the information in the table?
F.Felicia spends 10% of her monthly budget on clothes and food.
G.Felicia spends 25% of her monthly budget on her car payment.
H.Felicia spends 20% of her monthly budget on college savings.
J.Felicia spends 50% of her monthly budget on her car payment and cell phone.
I'm not really good at math and I'm doing a test online right now and I am very confused.
Answer:
The answer is J.
Step-by-step explanation:
50% of 800 is 400.
125+275=400
please help me please please nice brainly people pls
Answer:
I think your answer is B= 12.
Step-by-step explanation:
Its x times 1 .33333 = y
brainliest?
elements of {1,2,3,4,6,12} and {4,6,8,10}
Step-by-step explanation:
A ={1,2,3,4,6,12}
B={4,6,8,10
[tex]A \cup B=[/tex]{1,2,3,4,6,8,10,12}
I'm dumb, please help me.
Answer:
3/4
Step-by-step explanation:
15/20 is 3/4. therefore, according to the previous data, it is 3/4.
P.S. I looked at your answers and you cannot just spam random answers. thats rude and it violated the honor code. how would you feel if you posted a question and the answer was just random letters. and then you failed your test. thats not nice. and you are on canvas, because i use it too, and i know what it looks like. you cannot cheat on a test, as this is not what Brainly is for. im just so dissapointed because you disrespect others.
Joan wants to start an IRA that will have $860,000 in it when she retires in 29-years. How much should she invest annually in her IRA to do this if the interest is 8% compounded annually?
Answer:
Annual deposit= $8,271.94
Step-by-step explanation:
Giving the following information:
Future Value (FV)= $860,000
Number of periods= 29 years
Interest rate= 8% = 0.08
To calculate the annual deposit, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= annual deposit
Isolating A:
A= (FV*i)/{[(1+i)^n]-1}
A= (860,000*0.08) / [(1.08^29) - 1]
A= $8,271.94
How can you tell that the inequality 3x - 1 > 3x + 2 has no solution just by looking at the terms in the inequality? Please help. I cant do math!
Answer:
A
Step-by-step explanation:
You want to double the 3 into the right square. Then add 15. After that, move the 7 into the 10 square.And there you go. You got 19-
What is -3(5+5)>5x?
Answer:
The answer is x < -6
hope that helps
-3(5+5)>5x
-15+-15>5x
-30>5x
5x<-30
Divide both side by 5
5x÷5 < -30÷5
x<-6
Answer:
-15 is the incorrect answer the correct answer is x < --6
Step-by-step explanation: Simplify 5+55+5 to 1010.
-3\times 10>5x−3×10>5x
2 Simplify -3\times 10−3×10 to -30−30.
-30>5x−30>5x
3 Divide both sides by 55.
-\frac{30}{5}>x−
5
30
>x
4 Simplify \frac{30}{5}
5
30
to 66.
-6>x−6>x
5 Switch sides.
x<-6x<−6
Question
Help me -.8+ 2X = .3 - x
Step-by-step explanation:
2x+x=.3+.8
3x= 1.1/:3
x=0.366
Answer:
x = -2.566667
Step-by-step explanation:
simplify both sides
8 + 2x = 0.3 - x
8 + 2x = 0.3 + - x
2x + 8 = - x + 0.3
add x to both sides
2x + 8 + x = - x + 0.3 + x
3x + 8 = 0.3
subtract 8 from both sides
3x + 8 - 8 = 0.3 - 8
3x = -7.7
divie both sides by 3
3x/3 = -7.7/3
x = -2.566667
What is the value of the question mark in the picture below .
Answer:
84 degrees
Step-by-step explanation:
Vertical angles, then corresponding
complete the table of values for y=x3+x2-6x
Answer:
y= x ^3 - 4x
Step-by-step explanation:
Regroup terms.
y=x^3 +2x−6x
Simplify x^3 +2x−6x to x^3 −4x.
AAAAANNNNNnnNNND the answer is
y= x^3 - 4x
IN GRAPH
Maliah goes to an electronics store. Let y represent the price of a laptop and let z represent the price of a television. The equation
y=32 + 12 relates the prices.
Answer:
hi
Step-by-step explanation: