The zeros of the quadratic function f(x) = 2x² + 8x – 3 is x = -2 - √11/4 and x = -2 + √11/4
What is a quadratic function?A quadratic function is in the form:
y = ax² + bx + c
Given that:
f(x) = 2x² + 8x - 3, hence:
The zero is at:
2x² + 8x - 3 = 0
2x² + 8x = 3
Dividing through by 2:
x² + 4x = 3/2
add to both sides 4:
(x + 2)² = 3/2 + 4
(x + 2)² = 11/4
x + 2 = ±√11/4
x = -2 ±√11/4
The zeros of the quadratic function f(x) = 2x² + 8x – 3 is x = -2 - √11/4 and x = -2 + √11/4
Find out more on quadratic function at: https://brainly.com/question/1214333
Answer:
x = [tex]x=-2-\frac{11}{2}[/tex] and [tex]x=-2+\frac{11}{2}[/tex]
Step-by-step explanation:
I got it right on edge
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction In ΔABC, c = 5. 4, a = 3. 3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer. 2. 0 units and 4. 6 units 2. 1 units and 8. 7 units 2. 3 units and 7. 8 units 2. 6 units and 6. 6 units.
The length 2.3 and 7.8 units
We have given that ΔABC, c = 5. 4, a = 3. 3, and measure of angle A = 20 degrees.
What is the formula for low of cosine?The Law of Cosines, which tells us
[tex]a^{2}=b^{2} +c^{2} -2bccosA[/tex]
giving us a quadratic equation for b we can solve. But let's do it with the Law of Sines as asked.
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
We have c,a,A so the Law of Sines gives us sin C
[tex]sinC=\frac{csina}{a} =\frac{5.4sin20}{3.3} =0.5597[/tex]
There are two possible triangle angles with this sine, supplementary angles, one acute, one obtuse
[tex]C_{a}=arcsin(0.5597)=34.033^{0}[/tex]
[tex]C_{0}=180-C_{a} =145.96^0[/tex]
Both of these make a valid triangle with A=20°. They give respective B's:
[tex]B_{a}=180-A-C_{a} =125.96^0[/tex]
[tex]B_{0}=180-C_{0} =14.033^0[/tex]
So we get two possibilities for b:
[tex]b=\frac{asinB}{sinA} \\\\b_{a} =\frac{3.3sin125.96}{sin 20} \\\\b_{a}=7.8\\\\ b_0=2.3[/tex]
2.3 units and 7.8 units
Therefore we get the length 2.3 and 7.8 units
To learn more about the low of sine and cosine visit:
https://brainly.com/question/4372174
Answer: 2.3 units and 7.8 units
Let's check it with the Law of Cosines:
There's a shortcut for the quadratic formula when the middle term is 'even.'
Looks good.
x squared minus 8 equals 8
[tex] {x}^{2} - 8 = 8 \\ [/tex]
x^2 - 8 + 8 = 8 + 8
x^2 = 16
x = √16
x = 4
[tex]{\large{\red{\mapsto{\maltese{\underline{\green{\boxed{\blue{\underbrace{\overbrace{\pink{\pmb{\bf{Answer:}}}}}}}}}}}}}}[/tex]
[tex] \blue{ {x}^{2} - 8 = 8}[/tex]
[tex] \purple{ {x}^{2} - 8 + 8 = 8 + 8}[/tex]
[tex] \red{ {x}^{2} = 16}[/tex]
[tex] \green{ \sqrt{ {x}^{2} } = \sqrt{16} }[/tex]
[tex] \pink{x = 4}[/tex]
PLEASE HELP ME BY TODAY ((UNIT RATE)) I WILL GIVE BRAINLIEST, WORTH 20 POINTS
Answer:
80
Step-by-step explanation:
48 ÷ 6 = 8 per hour
8 x 10 hours = 80 dogs
Answer: Steve can train 80 dogs.
Step-by-step explanation:
How many dogs he can train divided by how many hours is: 48/6 = 8.
He is able to train 8 dogs per hour. So: 8 x 10 = 80.
-5=y-7 divided by 9 please help I really need this
Step-by-step explanation:
Our equation;
[tex]-5=\frac{y-7}{9}[/tex]
Multiply each side by 9 to remove the fraction;
[tex]-45=y-7[/tex]
Add 7 to each side;
[tex]\boxed{-38=y}[/tex]
What is 68% as a fraction in its simplest form?
Answer:
17/25
Step-by-step explanation:
68/100
divided by 2
34/50
divided by 2
17/25
and 17/25 is as simplified as it's going to get.
Ethan is observing an amusement park ride where the riders go around in a counterclockwise circular motion. The
carts take 2 seconds to complete a full rotation. The center of the ride is 24 feet above the ground as shown in the
diagram, and the cart Ethan is observing is labeled X
A sinusoidal equation can be used to describe the height because the height depends on a periodic motion, and the equation can be written as:
h(t) = 13ft*sin(pi*t) + 24ft
Why a sinusoidal equation can be used?Remember that the sine function has a periodicity, such that:
sin(x + 2pi) = sin(x).
So, for a circle where if you do a complete rotation you end in the initial place, so there can be a relation between the height and a sinusoidal equation.
Notice that the initial position is 24ft above the ground, so we can write this, at the moment, as:
h(x) = Asin(n*t) + 24ft
A is the amplitude, it defines the maximum height and minimum height, both depend on the radius (the maximum height is 24ft plus the radius, the minimum height is 24ft minus the radius) then we write:
h(t) = 13ft*sin(kt) + 24ft
k depends on how much time takes to do a full rotation. We know that the sine function does a "complete cycle" in 2pi, while the wheel does a full rotation in 2 seconds, then we have that:
k*2 = 2pi
k = (2pi)/2s = pi
Then the sinusoidal equation that represents the height is:
h(t) = 13ft*sin(pi*t) + 24ft
If you want to learn more about sinusoidal equations, you can read:
https://brainly.com/question/9478364
A rhombus where the left side of the horizontal diagonal has length 2 meters and the right side of the horizontal diagonal has length 2 meters. The top of the vertical diagonal has length 5.5 meters and the bottom of the vertical diagonal has length 5.5 meters.
What is the area of the rhombus?
11 m2
15 m2
22 m2
44 m2
PLEASE HURRY
Answer:
15 m2 is the answer
Step-by-step explanation:
The side of a rhombus is 15 m2. If the length of one diagonal of the rhombus is 8 cm, then find length of the other diagonal. The side of a rhombus is 15 m2. If the length of one diagonal of the rhombus is 8 cm, then find length of the other diagonal. so, the answer is 15 m2
Answer: 22 m2
Step-by-step explanation:
What is 20% of 45?
Thank you for answering this question.
Answer:
9
Step-by-step explanation:
cuz yes
Hi can someone help me to solve this? I would be so appreciated if you willing to help me
Nora and Farhan were asked to simplify (2x²/y)³
Nora wrote this : (2x²/y)³ = 2x⁶/y³
Farhan wrote this : (2x²/y)³ = 8x⁵/y
Both Nora and Farhan obtained the wrong solutions.
(i) Highlight the possible misconceptions that Nora and Farhan might have.
Nora's misconceptions:
Farhan's misconceptions:
(ii) provide the correct solution :
Answer:
HOPE ITS HELPFUL TO yours
game have total?
3) At a bake sale there were 52 items sold total. If 24 of the items sold were cookies and the rest
were brownies what is the ratio of brownies sold to cookies sold?
Answer:
the ratio is easy to find if you subtract 52 to 24 which is 28 so the ratio is 28 to 24
For what value of c does x^2−2x−c=4 have exactly one real solution?
PLEASE HELP!!!!!!!
Answer:
-5
Step-by-step explanation:
Moving all terms of the quadratic to one side, we have
[tex]x^2-2x-(c+4)=0[/tex].
A quadratic has one real solution when the discriminant is equal to 0. In a quadratic [tex]ax^2+bx+d[/tex], the discriminant is [tex]\sqrt{b^2-4ad}[/tex].
(The discriminant is more commonly known as [tex]\sqrt{b^2-4ac}[/tex], but I changed the variable since we already have a [tex]c[/tex] in the quadratic given.)
In the quadratic above, we have [tex]a=1[/tex], [tex]b=-2[/tex], and [tex]d=-(c+4)[/tex]. Plugging this into the formula for the discriminant, we have
[tex]\sqrt{(-2)^2-4(1)(-(c+4))[/tex].
Using the distributive property to expand and simplifying, the expression becomes
[tex]\sqrt{4-4(-c-4)}=\sqrt{4+4c+16}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{20+4c}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{4}\cdot\sqrt{5+c}\\~~~~~~~~~~~~~~~~~~~~~~=2\sqrt{c+5}.[/tex]
Setting the discriminant equal to 0 gives
[tex]2\sqrt{c+5}=0[/tex].
We can then solve the equation as usual: first, divide by 2 on both sides:
[tex]\sqrt{c+5}=0[/tex].
Squaring both sides gives
[tex]c+5=0[/tex],
and subtracting 5 from both sides, we have
[tex]\boxed{c=-5}.[/tex]
Tell weather the angles are adjacent or vertical then find the value of X
Answer:
The angles are adjacent (next to each other). Because they are adjacent, the angles equal 180 when added together. Therefore, X = 180-34. X = 146.
Hope this helps, and good luck with math! Have a great day/night :D
ILL GIVE BRAINLEST #20 please, how do I know if it’s similar or not? Is it similar?
Answer:
You can know if the shapes are similar if the are the same type of shape, have proportional side lengths, congruent corresponding angles (the angles are in the same place proportional to the shape and have the same amount of degrees), and equal scale factors.
In number 19, the polygons are similar because they have proportional side lengths and congruent corresponding angles.
Number 20's trapezoid A and B are not similar because the side lengths are not proportional to each other ( 2 is half of 4, 4 is not half of 6)
Hope this helps!
I rlly need help on this
Answer: 130, sorry if its wrong
Step-by-step explanation:
8 x 5 = 40 --> 40 x 3 1/4 = 130
What is the surface area of this prism? 14ft 10ft 10ft 8ft 6ft 6ft 4ft
Answer:
The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.
Step-by-step explanation:
i dont know the base and height because you dont have a picture provided so you can use this as help
(m+n)^2-(m+2)+mn*(n+2)+2n(n+2) pleae factor this
Answer:
mn^2+3n^2+4mn+4n+m^2-m-2
Using the following information, write the equation in point-slope form. A line passes through the point (-2, 1) and has a slope of -4.
[tex]\mathbb{FINAL\;ANSWER:}[/tex]
[tex]\huge\boxed{\sf{y-1=4(x+2)}}[/tex]
[tex]\mathbb{SOLUTION\;WITH\;STEPS:}[/tex]
Hi! Hope you are having a nice day!
We are given:
Slope of the lineA point that it passes throughCan we write the equation of the line in Point-Slope Form? Sure!
y-y₁=m(x-x₁)
y-1=-4(x-(-2)
y-1=-4(x+2)
Hope you could understand everything.
#CarryOnLearning
HELP PLSSS ASAP!!!!!!
Answer: p=5+3/2 or p=5-3/2
Step-by-step explanation:
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: {p}^{2} - 10p + 7 = 0[/tex]
Now, let's use Quadratic formula :
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ - ( - 10) \pm \sqrt{ {( - 10)}^{2} - 4(1 \times 7) } }{2 \times 1} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ 10 \pm \sqrt{ 100- 28 } }{2 } [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ 10 \pm \sqrt{ 72 } }{2 } [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ 10 \pm6 \sqrt{ 2 } }{2 } [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ 2(5 \pm3 \sqrt{ 2 }) }{2 } [/tex]
[tex]\qquad \sf \dashrightarrow \:x = (5 \pm3 \sqrt{ 2 }) [/tex]
So, the required roots are :
[tex]\qquad \sf \dashrightarrow \:x = 5 + 3 \sqrt{ 2 } [/tex]
and
[tex]\qquad \sf \dashrightarrow \:x = 5 - 3 \sqrt{2} [/tex]
Find the unknown length x in the right triangle, to the nearest tenth.
Answer:
11.3
Step-by-step explanation:
The side opposite the given angle is unknown. The hypotenuse is also given. The trig function that relates the angle, opposite side, and hypotenuse is the sine function:
Sin = Opposite/Hypotenuse
sin(39°) = x/18
x = 18·sin(39°) ≈ 11.3
Part A: Write an equivalent system of equations.
Part B: Justify why the system you wrote is equivalent.
Answer:
2/4, 4/8, 8/16, 16/32
Step-by-step explanation:
2/4
2x2/4x2 = 4/8
4x2/8x2 = 8/16
8x2/16x2 = 16/32
if x=10 what is the value of y in the equation 3x+5y=60
Given :-
x = 103x + 5y = 60[tex] \\ \\ [/tex]
To find :-
value of y[tex] \\ \\ [/tex]
Solution :-
[tex] \\ [/tex]
[tex] \looparrowright \sf3x + 5y = 60[/tex]
Put value of x in the equation!
[tex] \\ [/tex]
[tex] \looparrowright \sf3(10)+ 5y = 60[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf3 \times 10+ 5y = 60[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf30+ 5y = 60[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf5(6 + y) = 60[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf(6 + y) = 60 \div 5[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf6 + y= \dfrac{60}{5} [/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf6 + y=\cancel \dfrac{60}{5} [/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf6 + y= \dfrac{12}{1} [/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf6 + y=12[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf y=12 - 6[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \bf y=6[/tex]
[tex] \\ [/tex]
Verification:-
[tex] \\ [/tex]
[tex] \looparrowright \sf3x + 5y = 60[/tex]
Put value of x and y.
[tex] \\ [/tex]
[tex] \looparrowright \sf3(10)+ 5(6) = 60[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf3 \times 10+ 5(6) = 60[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf30+ 5(6) = 60[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf30+ 5 \times 6= 60[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \sf30+ 30= 60[/tex]
[tex] \\ [/tex]
[tex] \looparrowright \bf60= 60[/tex]
LHS = RHS
HENCE VERIFIED!
2. In an arithmetic sequence t, = 1,-1+7. If t = -5 determine the values of l, and tzo. Show the calculations
that lead to your answers.
PLEASE HELP
Answer:
10
Step-by-step explanation:
t+1/2t-1=5/7
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
WILL GIVE BRAINLIEST IF CORRECT
Simplify 2s + 4 + (-6s) + 10
-4s + 14
4s + 14
10s
18s
Answer:
−
2
(
2
−
7
)
Step-by-step explanation:
Let's first write out
2s+4+(-6s)+10
now simplify
-4s+14
again
now correct
Given △~△
Which statement is true?
Select one:
==
+=+=+
⋅=⋅=⋅
==
Answer:
c
Step-by-step explanation:
it’s equal
The sum of two numbers is 45. One number is
8 more than the other one. Find the numbers.
Answer:
6and 7,8,9,10 CORRECT ME IF I'M WRONG
16 inches to 5 feet as a fraction in simplest form.
Answer:
1 feet = 12 inches
therefore ,
5 feet = 5 × 12 = 60 inches
Now ,
16 inches to 60 inches ,
[tex] \frac{16}{60} \div \frac{4}{4} = \frac{4}{15} \\ [/tex]
hope helpful~
Answer: 6 1/3
Step-by-step explanation: 16 inches = 1 foot and 4 inches + 5 feet = 6' 4" 6 4/12 simplify = 6 1/3
The ratio of males to females is 3:4. How many females are there if there are..
i. 3 males
ii. 6 males
Answer:
i) 4 females
ii) 8 females
Step-by-step explanation:
1. Ratio of males= 3x
3x = 3
Thus, x = 1
If there are 3 males, there will be 4 females
2.Rato of males= 3x
3x = 6
Thus x = 2 [6 divided by 3]
4x = 4 x 2 = 8
If there are 6 males, there would be 8 females.
Triangle ABC has angle measures as shown below. Using the information in the diagram, and the value of x that you calculated in Question 2, find the measure of Angle C.
In your answer, give the measure of Angle C and explain how you calculated it.
Answer:
x=29
Step-by-step explanation:
180-87=93
93=3x+6
-6 -6
--------------
93=3x
/3 /3
-------------
29=x
x=29
*all angles in a triangle add up to 180. So, 35+52=93. 180-93=87.
C=87
what is the answer to 5 + 7f = 33
Answer:
f=4
Step-by-step explanation:
so, when we do this problem notice that there is a variable this can mean a lot of things but in this case, it just means were solving for f so we first move the constant (5) to the right-hand side and change its sign then we subtract 33 from 5 to get 28 so the equation would look like 7f = 33-5
to get 7f = 28 and now for the last step you divide both sides of the equation to get f = 4
Hope this helped :)
Find the value of x.
Answer: 30
Step-by-step explanation: