Use the quadratic formula to determine the exact solutions to the equation x^2-4x-8=0
Answers
The answer is 2+2√3 or 2-2√3
Answer:
[tex]x = 2[/tex]±[tex]\sqrt{12}[/tex]
Step-by-step explanation:
Given the following equation ax^2 + bx + c = 0, the quadratic formula states that the solution to that equation is going to be given by:
[tex]x1 = \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]x1 = \frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
In this case, a=1, b=-4 and c=-8. Therefore:
[tex]x1 = \frac{4+\sqrt{(-4)^{2}-4(1)(-8)} }{2}[/tex]
[tex]x1 = \frac{4+\sqrt{48}}{2}[/tex]
[tex]x1 = 2+\sqrt{12}[/tex]
[tex]x2 = \frac{4-\sqrt{(-4)^{2}-4(1)(-8)} }{2}[/tex]
[tex]x2 = \frac{4-\sqrt{48}}{2}[/tex]
[tex]x2 = 2-\sqrt{12}[/tex]
Therefore the solutions are:
[tex]x = 2[/tex]±[tex]\sqrt{12}[/tex]
Related Questions
Which of the following functions is shown in the graph below?
y = (x - 1)^2 + 2
y = -2(x - 1)^2 + 2
y = 2(x + 1)^2 + 2
y = (x + 1)^2 + 2
Answers
#2
Step-by-step explanation:
it is opening downwards so the number multiplying the function must be negative (in this case it is -2)
Answer:
y = -2(x - 1)² + 2
Step-by-step explanation:
recall that the vertex form of a quadratic equation is :
y = a(x - h)² + k, where (h, k) is the coordinate of the vertex (i.e maxima point)
from the graph we can see that the vertex is at x = 1, y = 2
hence the answers that are valid would have h = 1 and k = 2
right away by observing the answers, we can see that the last 2 choices have h = (-1) and so these are NOT the answers.
To decide between the first 2 choices, we observe from the given graph, that when x=0, y=0.
The only choice which satisfies this is the 2nd option
Proof:
for y = -2(x - 1)² + 2, when x = 0,
y = -2(0 - 1)² + 2
y = -2(- 1)² + 2
y = -2(1) + 2 = -2 + 2 = 0 (Proven to be valid)
Sanity check: check the first choice
y = (x - 1)² + 2
when x = 0,
y = (0- 1)² + 2
y = 1 + 2 ≠ 0 (not the answer)
Pat needs boards that are one half foot long. Which equation shows how many one half foot pieces he can get from a four foot long board
Answers
Answer:
4/.5 = 8
Step-by-step explanation:
You can solve this by adding up .5 8 times to equal 4. Another way to look at it is that you have 4 individual pieces that are a foot long and you decide to split all of them in half. Let me know if you have any other questions.
Answer:
The equation that shows that is the division between 4 and 0.5 as:
[tex]\frac{4}{0.5}[/tex]
Step-by-step explanation:
First, it is necessary to know that one half foot is equivalent to 0.5 foot.
We can solve this using a rule of three in which we know that 1 piece has one half foot long, then 4 foot long how many pieces have. This is:
1 board ----------- 0.5 foot
X ------------ 4 foot
Where X is the number of pieces that he can get from a four foot long board.
Solving for X, we get:
[tex]X = \frac{4*1}{0.5} = \frac{4}{0.5}[/tex]
So, the equation that shows how many one half foot pieces he can get from a four foot long board is:
[tex]X=\frac{4}{0.5}[/tex]
Simplify remove all perfect squares from inside the square root 125
Answers
Answer:
[tex]5\sqrt{5}[/tex]
Step-by-step explanation:
We start by factoring 125 and look for a perfect square:
125= 5*5*5=[tex]5^{2} *5[/tex].
This allow us to simplify the radical:
[tex]\sqrt{125} = \sqrt{5^{2} *5}[/tex]
So we have:
[tex]\sqrt{5^{2} *5} =5\sqrt{5}[/tex]
What is the equation that passes through (4, 3) and (2, -1)?
Y = 2x - 5
y = 4x -13
y = 6x+4
y = 1/2 x -2
Answers
Answer:
y = 2x - 5
Step-by-step explanation:
We are to find the equation of line the line which passes through the points (4, 3) and (2, -1).
Finding the slope:
Slope = [tex]\frac{3-(-1)}{4-2} =2[/tex]
Substituting the coordinates of one of the given points and slope in the standard form of an equation to find the y intercept.
[tex]y=mx+c[/tex]
[tex] -1 = 2 (2) + c \\\\ c = - 5 [/tex]
So the equation of the line would be [tex]y=2x-5[/tex]
Answer: first option.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
To find "m", we need to substitute the coordinates of the points (4, 3) and (2, -1) into this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can identify that:
[tex]y_2=-1\\y_1=3\\x_2=2\\x_1=4[/tex]
Then:
[tex]m=\frac{-1-3}{2-4}\\\\m=2[/tex]
To find "b" we must substitute the slope and one of the given points into [tex]y=mx+b[/tex] and solve for "b". Then, this is:
[tex]3=2(4)+b\\\\3-8=b\\\\b=-5[/tex]
Therefore, the equation of this line is:
[tex]y=2x-5[/tex]
intersecting lines that are formed as a right angle are defined as?
Answers
Answer:
Perpendicular
Step-by-step explanation:
Definition of perpendicular lines:
Lines that intersect forming a right angle are perpendicular lines.
Answer:
Perpendicular
Step-by-step explanation:
Is 36 a perfect square?
Answers
Answer:
yes
Step-by-step explanation:
6 times 6 = 36
Answer: Yes
Step-by-step explanation: Yes, it is a perfect square of 6. 6 x 6 = 36.
1. Evaluate cos-1 (tan (0))
Answers
Answer:
pi/2
Step-by-step explanation:
Arccos(tan(0))
Arccos( 0) since tan(0)=0
Arccos(0)=pi/2 since cos(pi/2)=0 and the restricted domain of cosine is [0,pi].
Answer:
1
Step-by-step explanation:
First of all go one step at a time. Find tan(0). For this question, you can use your calculator.
Tan(0) = 0 That's because the opposite side has a length of 0 and the tangent's definition is
Tan(x ) = opposite side / adjacent side. The opposite side and the adjacent side are part of the same length. There is no real opposite side.
=========
Now you are down to cos-1(0)
If you put that into your calculator like this
2nd Function
cos-1(
0
)
=
You will get 1
Which of the following ordered pairs represents a solution to the linear
inequality y > 2x - 3?
O A. (3,2)
O B. (9,12)
O C. (4,4)
O D. (2,5)
Answers
Answer:
O D. (2,5)
Step-by-step explanation:
y > 2x - 3
Substitute the points into the inequality and see if it is true
(3,2)
2 > 2(3) - 3
2> 6-3
2>3 False
(9,12)
12 > 2(9) - 3
12> 18-3
12>15 False
(4,4)
4 > 2(4) - 3
4> 8-3
4>5 False
(2,5)
5 > 2(2) - 3
5> 4-3
5>1 True
Answer:D
Step-by-step explanation:
How many roots does the polynomial function, y = (x + 4)(x-2)(x+7) have?
A. 3
B. 1
C. 2
D. A
Answers
Answer:
A. 3Step-by-step explanation:
The polynomial y = (x + 4)(x - 2)(x + 7) has 3 roots.
y = 0 ⇒ (x + 4)(x - 2)(x + 7) = 0 ⇔ x + 4 = 0 ∨ x - 2 = 0 ∨ x + 7 = 0
x + 4 = 0 subtract 4 from both sides
x = -4
x - 2 = 0 add 2 to both sides
x = 2
x + 7 = 0 subtract 7 from both sides
x = -7
The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots: -4, 2, and -7.A. 3
The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots, which can be found by setting y to zero and solving for the values of x that make the function equal to zero. When you set y to zero, the equation becomes 0 = (x + 4)(x - 2)(x + 7), and the roots are x = -4, x = 2, and x = -7. Hence, the correct answer to the question of how many roots the polynomial function has is:
A. 3
One-third of Sharon's land has
farm animals. One-fifth of the farm
animals are chickens. Which
model shows what fraction of
Sharon's land has chickens?
Answers
SEE PHOTO. Based on the diagram, all of the following are true except...
A) cos38 = 24/x
B) sin52 = 24/x
C) cos38 = x/34
D) cos52 = x/24
Answers
Answer:
Option D) cos52 = x/24
Step-by-step explanation:
In this problem angle of 38 degrees and angle of 52 degrees are complementary angles
so
38°+52°=90°
therefore
cos(38°)=sin(52°)
we know that
see the attached figure with letters to better understand the problem
In the triangle ABD
cos(38°)=24/x ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse
Remember that
cos(38°)=sin(52°)
so
sin(52°)=24/x
In the right triangle ABC
cos(38°)=x/34 ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse
In the right triangle ABD
Applying the Pythagoras Theorem
[tex]BD=\sqrt{x^{2}-576}\ units[/tex]
[tex]cos(52\°)=(\sqrt{x^{2}-576})/x[/tex]----> The cosine of angle of 52 degrees is equal to divide the adjacent side to angle of 52 degrees by the hypotenuse
Could Triangle JKL be congruent to Triangle XYZ? Explain.
Answers
Answer:
Im pretty sure its C
Step-by-step explanation:
because when u line up the the right angles u see the hypotenuse and leg of another triangle is the same
The given triangles are not congruent since the hypotenuse of one triangle is equal to the length of leg of another triangle.
What is congruency?Congruent triangles are triangles having both the same shape and the same size.Types of congruencies are SSS, SAS, AAS, ASA, RHS.How to find whether ΔJKL and ΔXYZ are congruent?For two triangles two be congruent, we need to check the the equality of corresponding sides and angles.Here the hypotenuse of ΔJKL is 10 units and one side(not the hypotenuse) of ΔXYZ is 10So the corresponding sides of the triangles are not equal.
So the triangles are not congruent.
So, option C is correct.
Find more about "Congruency" here: brainly.com/question/2938476
#SPJ2
The length of a rectangular is 7/10 ft .and the width is 1/5ft what is the perimeter
Answers
[tex]\huge\boxed{1 \frac{4}{5}\ \text{ft}}[/tex]
Explanation:Change [tex]\frac{1}{5}[/tex] so that is has a common denominator. [tex]\frac{1*2}{5*2}=\frac{2}{10}[/tex]
Make an equation. [tex]\frac{7+7+2+2}{10}[/tex]
Add. [tex]\frac{14+4}{10}[/tex]
Add. [tex]\frac{18}{10}[/tex]
Divide both sides by 2. [tex]\frac{9}{5}[/tex]
Convert to a mixed number. [tex]1 \frac{4}{5}[/tex]
Answer:
1 4/5 ft.
Step-by-step explanation:
Change 7/10 into 70
Change 1/5 into 20
( It will be easier to find perimeter this way )
Formula: P=2(l+w)
P=2(l+w)=2·(70+20)=180
Then, you change the 180 back into a fraction to get 1 4/5.
AB || CD. Find the measure of
Answers
Step-by-step explanation:
solve the equation:
5x-10=4x+20
Answer:
The correct answer is option B. 140
Step-by-step explanation:
From the figure we can see that,
AB ║ CD
To find the value of x
From the figure we can see that,
<CFE = <BEF [Alternate interior angles are equal]
4x + 20 = 5x - 10
5x - 4x = 20 + 10
x = 30
To find the measure of <BEF
m<BEF = 5x - 10
= (5*30) - 10
= 150 - 10
= 140°
Therefore the correct answer is option B. 140
A die rolled. The set of equally likely outcomes is {1,2,3,4,5,6}. Find the probability of rolling an odd number.
Answers
Answer:
3/6 or 50%
Step-by-step explanation:
The probability of rolling an odd number from the dice numbered, {1,2,3,4,5,6} is 3/6.
6 numbers in all.
3 odd numbers.
3 even numbers.
Therefore, 3/6 or 50%.
what is the rate of change from x = pi x = 3pi/2
Answers
Answer: 3/2 (simplified: 1.5)
Step-by-step explanation:
X=pi
X=3pi/2
Remove pi from both equations because pi will cancel out each other then you will be left with the equation 3/2. So therefore the rate of change would be 3/2 simplified would be 1.5
wh as t is a prime numbers
Answers
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers
Step-by-step explanation:
Final answer:
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Prime numbers have many interesting properties and applications in mathematics.
Explanation:
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, it is a number that is only divisible by 1 and itself.
For example, the numbers 2, 3, 5, and 7 are prime numbers because they have no divisors other than 1 and themselves. On the other hand, the number 4 is not prime because it is divisible by 1, 2, and 4.
Prime numbers have many interesting properties and applications in mathematics, including their role in number theory and cryptography.
Find the geometric means in the following sequence.
-9,?,?,?,?,-9,216
Select one:
a. -144, -576, -2,304, -9,231
b. 36, 144, 576, 2,304
c. -720, -1,080, -1,440, -1,800
d. -36, -144, -576, -2,304
Answers
Answer:
Last choice. d.
Step-by-step explanation:
We are given the first term and the sixth term.
The first term is [tex]a_1=-9[/tex].
The sixth them is [tex]a_6=a_1r^5=-9216[/tex].
Let's solve for the common ratio, r.
[tex]-9r^5=-9216[/tex]
Divide both sides by -9:
[tex]r^5=1024[/tex]
Take the fifth root of both sides:
[tex]r=1024^{\frac{1}{5}}[/tex]
[tex]r=4[/tex]
So the common ratio is 4.
[tex]a_1=-9[/tex]
[tex]a_2=-9(4)=-36[/tex]
[tex]a_3=-9(4)^2=-144[/tex]
[tex]a_4=-9(4)^3=-576[/tex]
[tex]a_5=-9(4)^4=-2304[/tex]
[tex]a_6=-9(4)^5=-9216[/tex]
If WZYX is equal to PMLN describes two quadrilaterals, which other statement is also true? I NEED THIS ANSWER ASAP
A.WXYZ equal to LMNP
B.WXYZ equal to NPML
C.WXYZ equal to PNLM
D.WXYZ equal to MLNP
Answers
Answer:
C.WXYZ equal to PNLM
Step-by-step explanation:
Look at the given statement, WZYX is equal to PMLN.
WZYX is equal to PMLN. W corresponds to P.
WZYX is equal to PMLN. Z corresponds to M.
WZYX is equal to PMLN. Y corresponds to L.
WZYX is equal to PMLN. X corresponds to N
Now look in the choices. The letters must correspond like they do above.
W must correspond to P.
WXYZ equal to P...
X must correspond to N.
WXYZ equal to PN...
Y must correspond to L.
WXYZ equal to PNL...
Z must correspond to M.
WXYZ equal to PNLM
Answer: C.WXYZ equal to PNLM
Answer: C.WXYZ equal to PNLM
Two forces of 7 newtons and 11 newtons act on a body at an angle of 60° to each other. Find the magnitude of the resultant force to the nearest whole number.
Answers
Answer:
16 N
Step-by-step explanation:
If the 7 N force is at 0°, and the 11 N force is at 60°, then the components of the resultant force are:
Fₓ = 7 cos 0° + 11 cos 60° = 12.5
Fᵧ = 7 sin 0° + 11 sin 60° ≈ 9.53
The magnitude of the resultant force is:
F = √(Fₓ² + Fᵧ²)
F ≈ 15.7
Rounded to the nearest whole number, the magnitude is 16 N.
What is the simplified expression for 4^4 x 4^3/4^5
Answers
Write the slope-intercept form of the equation that passes through the point (-3, 5) and is perpendicular to the line y = 1/5x + 10 y = 5x + 10 y = -1/5x + 22/5 y = 1/5x + 28/5 y = -5x - 10
Answers
Answer:
y = -5x - 10Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================[/tex]
[tex]\text{We have}\ y=\dfrac{1}{5}x+10\to m_1=\dfrac{1}{5}\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{5}}=-5.\\\\\text{Put the value of a slope and the coordinates of the point (-3, 5)}\\\text{to the equation}\ y=mx+b:\\\\5=-5(-3)+b\\5=15+b\qquad\text{subtract 15 from both sides}\\-10=b\to b=-10\\\\\text{Finally:}\\\\y=-5x-10[/tex]
Suppose y varies directly as x, and y=2 when x=4. Which of the following statements is true?
Answers
Answer:
constant of variation = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 2 when x = 4
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
Answer:
The constant of variation is 1/2.
Step-by-step explanation:
y = kx where k is the constant of variation.
So k = y/x = 2/4 = 1/2.
How would you do number 12 and 15?
Answers
Answer:
[tex]x_1=x_2=-\dfrac{2}{3}[/tex]
Step-by-step explanation:
For the quadratic equation [tex]ax^2+bx+c=0[/tex] the discriminant is defined as
[tex]D=b^2-4ac[/tex]
and the quadratic formula for the roots gives us two roots:
[tex]x_1=\dfrac{-b-\sqrt{D}}{2a}[/tex]
and
[tex]x_2=\dfrac{-b+\sqrt{D}}{2a}[/tex]
For the equation [tex]9x^2 +12x+4=0[/tex] use quadratic formula to find roots:
[tex]D=12^2-4\cdot 9\cdot 4=144-144=0[/tex]
So,
[tex]x_1=x_2=\dfrac{-12\pm \sqrt{0}}{2\cdot 9}=-\dfrac{12}{18}=-\dfrac{2}{3}[/tex]
URGENT HELP MEEEEE!!!:D
Answers
Answer: C: 3rd degree polynomial wit 3 terms.
Step-by-step explanation: The polynomial has 3 terms and the highest degree is 3.
C. Third degree polynomial with three terms.
Terms are, by definition, the number of nonzero coefficients for powers of x. In this case, there are 3 nonzero coefficients (3 terms) because [tex]-1=-1x^0[/tex]. For example, [tex]2x^3[/tex] has one term, but [tex]0[/tex] has 0 terms.
The degree of a polynomial is the highest power involved in the expression. In this case, it's [tex]4x^3[/tex], so the degree is 3.
if sin(x-3)° / cos(2x+6) = 1, then the value of X is
Answers
Answer:
x = 29° + n·120° . . . or . . . 261° +n·360° . . . . for any integer n
Step-by-step explanation:
Multiplying by the denominator, the equation becomes ...
sin((x -3)°) = cos((2x+6)°)
The sine and cosine are equal when ...
(x -3) + (2x +6) = 90 + n·360 . . . . . for any integer n
3x +3 = 90 + n·360 . . . . . . . . . collect terms
x +1 = 30 +n·120 . . . . . . . . . . . .divide by 3
x = 29 + n·120 . . . . . . . . . . . . . . subtract 1
__
The sine and cosine are also equal when ...
(x -3) -(2x +6) = 90 + n·360
-x -9 = 90 +n·360
x = -99 -n·360
Since n can be any integer, this can also be written as ...
x = 261 + n·360
Possible values of x include {29, 149, 261, 269} +n·360 for any integer n.
_____
The graph shows solutions to sin(x-3)-cos(2x+6)=0, which has the same solutions as the given equation.
Suppose S and T are mutually exclusive events find P(S or T) if P(S)=1/3 and P(T)=5/12
Answers
Answer:
P(S or T)= 3/4
Step-by-step explanation:
Given:
S and T are mutually exclusive events
find P(S or T)
P(S or T)= P(S) + P(T)
= 1/3 +5/12
=4+5/12
=9/12
=3/4 !
Answer:
The value of P(S or T) is 3/4.
Step-by-step explanation:
It is given that S and T are mutually exclusive events. It means intersection of S and T is 0.
[tex]S\cap T=0[/tex]
[tex]P(S\cap T)=0[/tex]
We need to find the value of P(S or T). It means we have to find the probability of union of S and T.
[tex]P(S\cup T)=P(S)+P(T)-P(S\cap T)[/tex]
Substitute the given values in the above formula.
[tex]P(S\cup T)=\frac{1}{3}+\frac{5}{12}-(0)[/tex]
[tex]P(S\cup T)=\frac{4+5}{12}[/tex]
[tex]P(S\cup T)=\frac{9}{12}[/tex]
[tex]P(S\cup T)=\frac{3}{4}[/tex]
Therefore the value of P(S or T) is 3/4.
if kevin makes c toys in m minutes, how many toys can he make per hour
Answers
Answer:
[tex]\frac{60c}{m}[/tex]
Step-by-step explanation:
We can use the unity rule to solve this problem.
Number of toys made in m minutes = c
Number of toys made in 1 minute = [tex]\frac{c}{m}[/tex]
Number of toys made in 60 minutes = [tex]\frac{c}{m} \times 60 = \frac{60c}{m}[/tex]
Since 60 minutes = 1 hours, we can write:
Number of toys made in 1 hour = [tex]\frac{60c}{m}[/tex]
Therefore, we can say that Kevin makes [tex]\frac{60c}{m}[/tex] toys per an hour.
A girls' track team must run 3 miles on the first day of practice and 6 miles every day after that. The boys' team must run 5 miles every day of practice. The coach will order new javelins at the end of the day that each girl's total mileage surpasses each boy's. How many total miles will each girl have run by the time the coach orders the new equipment?
Answers
Answer:
The 4th day so 21 miles the girls would have to run
Step-by-step explanation:
Answer:
Each girl would have ran a total of 21 miles and boys would have ran a total of 20 miles by the end of the fourth day before the couch order new javelins.
Step-by-step explanation:
Girls track team
First day of practice=3 miles
Days afterwards= 6 miles
Boys track team
Everyday= 5 miles
coach will order new javelins at the end of the day that each girl's total mileage surpasses each boy's.
First day
Each girl total mileage= 3 miles
Each boy total mileage= 5 miles
Second day
Each girl total mileage= 3miles+6miles=9 miles
Each boy total mileage=5 miles+5 miles= 10 miles
Third day
Each girl total mileage= 3+6+6=15 miles
Each boy total mileage=5+5+5=15 miles
Fourth day
Each girl today mileage= 3+6+6+6=21 miles
Each boy total mileage=5+5+5+5= 20 miles
Difference=girls-boys
=21-20= 1 mile
The fourth day is the day each girl's total mileage(21 miles) surpasses each boy's total mileage(20 miles) with a total of 1 mile
Help me with question 4 and 5
Answers
I am not familiar with the grid below that, however. But the first part is:
25 + 4d = 225.