Answer:
Two real distinct solutions
Step-by-step explanation:
Hi there!
Background of the Discriminant
The discriminant [tex]b^2-4ac[/tex] applies to quadratic equations when they are organised in standard form: [tex]ax^2+bx+c=0[/tex].
All quadratic equations can be solved with the quadratic formula: [tex]x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}[/tex].
When [tex]b^2-4ac[/tex] is positive, it is possible to take its square root and end up with two real, distinct values of x.
When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.
When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.
Solving the Problem
[tex]3x^2+5x=-1[/tex]
We're given the above equation. It hasn't been organised completely in [tex]ax^2+bx+c=0[/tex], but we can change that by adding 1 to both sides to make the right side equal to 0:
[tex]3x^2+5x+1=0[/tex]
Now that we can identify the values of a, b and c, we can plug them into the discriminant:
[tex]D=b^2-4ac\\D=(5)^2-4(3)(1)\\D=25-4(3)(1)\\D=25-12\\D=13[/tex]
Therefore, because the discriminant is positive, the equation has two real, distinct solutions.
I hope this helps!
Can anyone help with this?
If P = (-3,5), find the image
of P under the following rotation.
90° counterclockwise about the origin
([?], [
[]
Enter the number that belongs in
the green box
Answer:
(-5 , -3)
Step-by-step explanation:
use formula of 90 degree counterclockwise rotation about the origin
formula:
(x , y) = (-y , x)
(-3 , 5) = (-5 , -3)
The required coordinate of the point after 90° clockwise rotation is (-5, -3).
What does it mean by rotation?A shape or item is rotated when it is spun around a certain point (center) without being moved in any other way. Size and shape are unaffected by rotation.
The given coordinate of the point is (-5, -3).
Counterclockwise rotation about the origin is given as,
(x , y) = (-y , x)
(-3, 5) = (-5 , -3)
Thus, the required coordinate of the point after 90° clockwise rotation is (-5, -3).
Learn more about rotation here:
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A circle with the centre (0,0) has an equation of x2 + y2 = 169
a. What is the radius?
Please Help I'll give brainliest
Answer:
259.8
Step-by-step explanation:
Simplify 6(x + 3).
6x + 3
x + 18
6x + 18
6x + 9
Answer:
the answer of this question is = 6x + 18
does the equation define y as a function of x? y^2 = 7 - x^2
The width of classroom is 4 meters less than the length, and the area is 192m^2. If the length is x m, find an equation in x and hence, find the dimensions of the classroom
Step-by-step explanation:
x(x-4) = 192
the Equation:
x²-4x -192 =0
=> (x-16) (x+12) =0
x= 16 or x= -12
since the x should be a possitive, so x = 16
the dimension :
the length = 16 m
the width = 12 m
Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root.
Answer:
[tex]y = \sqrt{ 900 - x\²[/tex]
Step-by-step explanation:
In the complete question, the area of the roller coaster is:
[tex]x\² + y^2 = 900[/tex]
Required
Solve for y
We have:
[tex]x\² + y^2 = 900[/tex]
Subtract [tex]x\²[/tex] from both sides
[tex]y^2 = 900 - x\²[/tex]
Take positive roots of both sides
[tex]y = \sqrt{ 900 - x\²[/tex]
Find the value of x and the measure of the exterior angle. (9x+16) (5x-14)
Answer:
[tex]x = 15 \: \: .....(5(15)- 14) = 61[/tex]
[tex](9x + 16 )= (5x - 14) + 90 \\ 9x - 5x = 90 - 14 - 16 \\ 4x = 60 \\ x = \frac{60}{4} \\ x = 15[/tex]
Evaluate the expression when a = 4 and c= -6
-a + 3c
Answer:
-22
Step-by-step explanation:
if a = 4, then it will be
-4 + 3(-6)
-4 - 18
which will be equal -22
4 + 3 × -6 = -22
Your welcome! :)
Please help me with this. Ill give you a brainliest.
Answer:
7. Circumcenter is (5,8)
8. Circumcenter= (-4,-5)
9. Circumcenter= (-4,9)
10. Circumcenter= (5.5, -5.5)
Two radar stations 2.5 miles apart are tracking an airplane. the straight-line distance between Station A and the plane is 7 miles. the straight-line distance between station B and the plan is 9 miles. What is the angle of elevation from Station B to the plane?
Answer: Hi the answer would be 32 Degrees
Step-by-step explanation:
Guys This is one of the most difficult question .
I salute the person who answer it correctly
The question goes like this :
The present price of a Camera is $32400. After day to day use, its price depriciates !! in such a way that its price will be $0 in 12 years ,, Then calculate the ptice of the Camera after 4 years.
Answer:
$21,600
Step-by-step explanation:
32400÷12=2700
2700×4=10,800
32400-10800=21600
Answer: $21,600
Step-by-step explanation: 32400÷12=2700
2700×4=10,80032400-10800=21600Points A(7, -5), B(-1, -2), and C(-4, 6) form triangle ABC on a coordinate plane. According to its sides, triangle ABC is a(n)
triangle
The answer is scalene
What is the solution to this equation? X/4 =-12
A. x = 48
B. X= -3
C. x = -48
D. X= 3
Answer:
C. x=-48
Step-by-step explanation:
x/4=-12
multiply both sides by 4
4x/4=4 (-12)
simplify
x=-48
what do you means by. India gate
Answer:
The India Gate (formerly known as the All India War Memorial) is a war memoria)
Step-by-step explanation:
it's a place
A deep-sea diver must descend and ascend in short steps to equalize pressure on his body. If
the diver rises toward the surface too fast, he may suffer from a physical condition called “the bends.”
Suppose the diver started at 100 feet below the surface and rose in five steps of 15 feet each. Use an integer
to describe his new position in relation to the water surface.
Answer:
15x=100?
Step-by-step explanation:
this equation would show how many steps it takes to get to the surface sorry if this isnt the answer u wanted
Answer:
-25
Step-by-step explanation:
he rose 75 feet from being under 100 feet of water, making him 25 feet below the water's surface
Complete the Steps to Solve the Equation -13x-11=-37
-13x-11=-37
-13x=
Answer:
x=2
Step-by-step explanation:
-13x-11=-37 Original equation
-13x=-26 Add 11 to both sides
x=2 Divide both sides by -13
A line's y-intercept is 1, and its slope is -5. What is its equation in
slope-intercept form?
help please
Which expression can go in the blank to make the equation true?
-2.9 + 2.8 + ____________ = 0
Answer:
+0.1
Step-by-step explanation:
when we subtract 2.9 and 2.8 we get -0.1 and to make it zero we have to keep +0.1
The circumference of a circle can be found using the formula C = 2r.
Which is an equivalent equation solved for r?
r = C
r = C(2)
r = r equals StartFraction C Over 2 pi EndFraction.
r = r equals StartFraction 2 pi Over C EndFraction.
Answer:
r = C/(2π)
Step-by-step explanation:
C = 2πr
Divide both sides by 2π
C/(2π) = r
r = C/(2π)
Given that the circumference of a circle, its radius r becomes r = C/2π.
Option C) r equals StartFraction C Over 2 pi EndFraction is the correct answer.
What is a circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges. The total length of the boundary of a circle is referred to as a circumference. It is expressed as;
C = 2πr
Where r is radius and π is constant pi ( π = 3.14 )
Now, if the circumference C = 2πr, lets make radius r the subject of the formula.
C = 2πr
Divide both sides by 2π
C/2π = 2πr/2π
C/2π = r
r = C/2π
Given that the circumference of a circle, its radius r becomes r = C/2π.
Option C) r = start fraction C over 2 pi end fraction is the correct answer.
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what is the slope of this line? y=-3x+1
Answer:
The slope is -3, also written as -3/1.
Answer:
-3
Step-by-step explanation:
it is simply the (m) in y = mx + b
m is the slope
and b is the y intercept
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Find the value of x in The parallelogram.
Answer:
48 degrees
Step-by-step explanation:
x+132 should be equal to 180, property of a parallelogram (and same side interior angles)
180-132=48
Answer:
x = 48
Step-by-step explanation:
Consecutive angles in a parallelogram sum to 180° , so
x + 132 = 180 ( subtract 132 from both sides )
x = 48
Put in in order from least to Greatest 3,-18,5,4,-2,6
A)-2,3,4,5,6-18
B)-2,18,3,4,5,6
C)-18,-2,3,4,5,6
D)3,4,5,6-2,-18
Answer:
A.
Step-by-step explanation:
-2,3,4,5,6-18 from least to greatest
How do you solve this equation ? 25 − 3 x = 40
Answer:
x = -5
Step-by-step explanation:
25 - 3x = 40
3x = -15
x = - 5
Answer:
x = -5
Step-by-step explanation:
25 − 3x = 40
-3x = 15
x = -5
The base of triangle M is four times the base of tri-
angle N, while the height of triangle N is half the
height of triangle M. The area of triangle M is how
many times that of triangle N ?
Answer:
two times
Step-by-step explanation:
ΔM: let 'h' = height; let '4b' = base
ΔN: let 'h/2' = height; let 'b' = base
Area (ΔM) = 2bh
Area (ΔN) = bh
Help With the answer Please
??????
Answer:
not sure
Step-by-step explanation:
Answer:
b) FIGURE A AND FIGURE B
Step-by-step explanation:
figure c has
all the sides equal so its not a rectangle
Scarlett can bake 10 cookies with each scoop of flour. Write an equation that shows the relationship between the scoops of flour x and the cookies y. Write your answer as an equation with y first, followed by an equals sign.
Substitute w = 4 into the following expression
10 – 4w
Answer:
-6
Step-by-step explanation:
Substitute as in replace "w" with 4
10-4(4)
Multiply -4 and 4
-16
10-16=-6
Hope this helps
Answer:
-6 it wouldnt let me post this without having 20 letters in my answer
Step-by-step explanation:
10 - 4*4 = -6.
in . 3.5 in 4 9 in 4 in . The triangular prism above has been created with two equilateral triangles and three congruent rectangles . The height of the triangles is 3.5 inches . Find the surface area of the triangular prism . square inches
Answer:
122 in²
Step-by-step explanation:
Applying,
S.A = bh+ bl+bl+bl............. Equation 1
Where S.A = Surface area of the prism, b = base of the triangle, h = height of the triangle, l = lenghth of the prism
From the question,
Given: b = 4 in, h = 3.5 in, l = 9 in
Substitute these values into equation 1
S.A = 4×3.5+9×4+9×4+9×4
S.A = 14+108
S.A = 122 in²
Hence the surface area of the prism is 122 in²
