Let us consider a quadratic equation αx² + βx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.
If Discriminant, D > 0, then roots of the equation are real and unequal.If Discriminant, D = 0, then roots of the equation are real and equal.If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.Where,
[tex]\quad\red{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}} [/tex]
Given Equation:-[tex]\red{\leadsto}\: \sf{2x^2 + 4x -7= 0} [/tex]
α = 2β = 4c = -7Now,
[tex]\quad\green{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}} [/tex]
[tex]\begin{gathered}\begin{gathered}\implies\quad \sf D = 4^2-4\times 2\times ( - 7) \end{gathered} \end{gathered} [/tex]
[tex]\begin{gathered}\begin{gathered}\implies\quad \sf D = 16-( - 56)\end{gathered} \end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf D = 16 + 56\end{gathered}[/tex]
[tex]\begin{gathered}\begin{gathered}\implies\quad \sf D = 72 \end{gathered} \end{gathered} [/tex]
Since, Discriminant, D > 0, then roots of the equation are real and distinct.
3.) Simplify the expression by combining like
terms: 45s^2 - 19 - s^2 + 16
please help i’m sick and don’t understand:(
[tex]45s^2-19-s^2+16\\=45s^2-s^2-19+16\\=s^2(45-1)-19+16\\=44s^2+(-19+16)\\=44s^2-3[/tex]
Hope that helps and hope you get better!
What is the opposite operation of squaring? Using this opposite operation, rewrite the equation from question 1 so s is by itself on one side of the equation.
50 POINTS!
The two main parts of an equation in Slope-Intercept Forrn are the Slope and the Y-Intercept.
A. True
B. False
Answer:
A
Step-by-step explanation:
Jeff had 1 A,4Bs and 2 C's what was he's gpa
Answer:
Hes Gpa Is that man is good. helps :0
Step-by-step explanation:
Directions: Express the number in scientific notation.
The human eye blinks an average of 4,200,000
times a year.
Answer:
count how many time you need to move the decimal point to only have 1 number on the left
4,200,000 = 6 times
4.2 × 10^6
A) 22.4
B) 43.7
C) 85.3
D) 4.75
Answer:
its should be b
Step-by-step explanation
mark brainlist
24 candy bars cost $48.
How much do 10
candy bars cost?
In a toy store, the ratio of the number of teddy bears to the number of dolls is 7:3 . If the store has 140 teddy bears , how many dolls are in the store?
Answer:
I prefer to set their units in order so it can help me;
Bears/Dolls7 Bears 140 bears
_______ = _______
3 Dolls x
⇒ 7 Bears x20 140 bears
_______ = _______ , 3(20) = 60 Dolls
3 Dolls x20 x
Solve for m:
(-11/6) + m = -2/9
M=
Step-by-step explanation:
(-11/6) + m = -2/9
m = -2/9 + 11/6
the last common multiple of 9 and 6 is 18.
so, we are bringing both fractions to .../18.
m = -2×2/18 + 11×3/18 = -4/18 + 33/18 = 29/18
Find the volume of the cylinder. Enter the answer EXACTLY as it appears on
your calculator. NO ROUNDING this time.
Answer:
653.45
Step-by-step explanation:
i really need help with my homework and its so hard can you help me plss here is question one m+43=38+46
Answer:
m = 41
Step-by-step explanation:
m + 43 = 38 + 46
m + 43 = 84 ( subtract 43 from both sides )
m = 41
Here is a system of linear equations
2x+3y=14
4x-3y=10
Which would be more helpful for solving the system: adding the two equations or subtracting one from the other?
Answer:
adding the 2 equations
Step-by-step explanation:
2x + 3y = 14 → (1)
4x - 3y = 10 → (2)
since the coefficients of the y- terms are opposites then adding will eliminate y
add (1) and (2) term by term
6x + 0 = 24
6x = 24 ( divide both sides by 6 )
x = 4
substitute x = 4 into either of the 2 equations and solve for y
substituting into (1)
2(4) + 3y = 14
8 + 3y = 14 ( subtract 8 from both sides )
3y = 6 ( divide both sides by 3 )
y = 2
solution is (4, 2 )
Larry is preparing jars of tomatoes from his garden. Each of his three sisters has asked for at least two jars of tomatoes, and Larry needs at least five jars for himself. i need help right now
if i tell you the truth i dont even know
Consider an urn with 7 black balls, 3 yellow balls, and 4 orange balls. If 3 balls are chosen randomly with replacement, what is the probability that the first is yellow, the second is orange, and the third is orange
Answer:
1.79% chance or [tex]\frac{6}{343}[/tex]
Step-by-step explanation:
7+3+4=14
chance of yellow [tex]\frac{3}{14}[/tex]
chance of orange [tex]\frac{4}{14}[/tex]
[tex]\frac{3}{14} * \frac{4}{14} *\frac{4}{14} = \frac{6}{343}[/tex]
i need help with this
Answer: 17 degrees
Step-by-step explanation: Because you have angle A= 163, you can tell that angle B is 17 degrees (sum of angles on one side of a straight line add up to 180). Line M and line N are parallel, so they have corresponding angles, making angle B and angle X are the same. See picture attached for my diagram :). hope this helped!
Part A: What do the x-intercepts and maximum value of the graph represent in context of the described situation?
Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and
profit for the company in the situation described?
Part C: What is an approximate average rate of change of the graph from x = 1 to x = 3, and what does this rate represent in
context of the described situation?
The x intercept of the given graph of the company's profit is where the curve of the graph crosses the x-axis.
How to determine the x-interceptIn this figure, the graph crosses the x-axis at x = 0 and x = 6
This represents the profit is 0 when the price is $0 and $6, respectively
The maximum valueThis represents the maximum profit that can be made.
From the graph, the maximum profit is $120
The increasing and the decreasing intervalFrom the graph, the graph increases from x = 0 to x = x = 3, and it decreases from x = 3 to x = 6
These intervals represent when the profit increases, and when it decreases
The average rate of changeThis is calculated as:
[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]
So, we have:
[tex]m = \frac{f(3) - f(1)}{3 - 1}[/tex]
[tex]m = \frac{f(3) - f(1)}{2}[/tex]
Substitute known values
[tex]m = \frac{120 - 60}{2}[/tex]
[tex]m = \frac{60}{2}[/tex]
Simplify
[tex]m = 30[/tex]
Hence, the average rate of change from x = 1 to x = 3 is a profit of $30 per unit sale
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Write the algebraic representation when the
scale factor is 8.
PLEASE HURRY I NEED HELP
Answer:
I think 58% I’m not 100% sure but yea
Step-by-step explanation:
I divided the number of votes for printed 71 by the total number of votes 122 so 71/122=.58 58%
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answer:
Based on the linear regression equation, the intercept means that for 0 missed classes, the expected test score is 98✓we know that,
y intercept exist when x = 0
so,
⇢y = -4x +98
⇢y = -4 x 0 +98
⇢y = 98
so , the expected test score is 98
Based on the linear regression equation, the slope means that for every missed class, the expected tast score decreases by 4 points✓when x = 0
y = -4(0) +98
when x = 1
y= -4(1) +98 = 94
when x = 2
y= -4(2) +98 = 90
we can see the decresement of 4 points
Based on the linear regression equation, as the number of days a student misses class increases the expected test score decreases ✓We can see that the increament in absent days lead to lower scores ( one class = 4 points)
For 0 clases
y=-0+98=98Option A is certified as correct
Here slope is -4So it decreasing not increasing
Option C is correct
Yes as the missed classes increase expected test decreasing as slope is negative.
Option F is correct
Multiply: (3xl-5)(-x + 4)
)+
Applying the distributive property, the expression becomes (3x)(-x) + (3x)(4) + (-5)(-x) + (-5)(4).
What is the simplified product in standard form?
px +
62 +
Answer:
Step-by-step explanation:
Multiply: (3x - 5)(-x + 4)
By applying the distributive property,
(3x - 5)(-x + 4)
= (3x)(-x) + (3x)(4) - (5)(-x) - (5)(4)
= -3x^2 + 12x + 5x - 20
= -3x^2 + 17x - 20
That is the simplified product in standard form.
Let's see
[tex]\\ \rm\longmapsto (3x-5)(-x+4)[/tex]
a(b+c)=ab-bc[tex]\\ \rm\longmapsto 3x(-x+4)-5(-x+4)[/tex]
[tex]\\ \rm\longmapsto -3x^2+12x+5x-20[/tex]
[tex]\\ \rm\longmapsto -3x^2+17x-20[/tex]
Your odometer reads 4,261 miles. You drive your car until the odometer reads 4,751 and your car used 25 gallons of gasoline during the trip.
About how many miles per gallon has your car been getting? Round up to the highest ten.
20
35
170
190
Answer:
35 gallons.
Step-by-step explanation:
Why? Bc it is the closest 4,751
HELP PLEASE i will give 25
Answer:
130°
.....
....................
How are the two shapes
similar?
Answer:
they arent
Step-by-step explanation:
maybe height or width
i dunno
Let g(x) = 3(x - 6)^2 + 1. Find the range of $g$.
Answer:
[1,∞)
Step-by-step explanation:
Let's try to plug in some numbers.
When solving a problem fo range, the best place to start is where you can let the (x - b) part = 0.
This is what I mean
3(x-6)² + 1
Let x = 6
3(0)² + 1 = 1
Look how we have a 0 inside the parentheses.
That's what I mean.
Now let's try using terms smaller than 6.
Now, let's try plugging in 5
3(-1)² + 1 = 4
Now try plugging in 4
3(-2)² + 1 = 13
Looks like we will just keep going up.
Now let's try using terms bigger than 6.
Plugging in 7
3(1)² + 1 = 4
Plugging in 8
3(2)² + 1 = 13
We just go up both ways because of the x squared term.
So our smallest value is at x = 6 where we have y = 1.
If we go either direction forever to the right or left the terms to get bigger, where it approaches infinity.
So, 1 will have parentheses as it can be reached and infinity will have parentheses as it is unreachable and goes on forever.
[1,∞)
- Simplify (3x - 5) + (5x + 1). O 8x - 6 O 8x +4 - O 8x - 4 O 2x - 4
Answer:
8x - 4
Step-by-step explanation:
3x - 5 + 5x + 1
8x - 4
There are 135 people in a sport centre.
73 people use the gym.
59 people use the swimming pool.
31 people use the track.
19 people use the gym and the pool.
9 people use the pool and the track.
16 people use the gym and the track.
4 people use all three facilities.
Given that a randomly selected person uses at least two facilities, what is the probability they
use all the facilities?
Answer:
1/9
Step-by-step explanation:
4 people use all three facilities, then
16 - 4 = 12 people use the gym and the track and do not use the pool;
9 - 4 = 5 people use the pool and the track and do not use the gym;
19 - 4 = 15 people use the gym and the pool and do not use the track.
At least two facilities use 4 + 12 + 5 + 15 = 36 people, 4 of them use all three facilities. Thus, the probability that a randomly selected person which uses at least two facilities, uses all the facilities is 4/36 which is equivalent to 1/9
A group of students must collect at least $150 to organize a science fair. They have already collected $30. Which graph best represents all remaining amounts of money, in dollars, that the students should still collect to organize the science fair?
Number line graph with a closed circle on 120 and shading to the right.
Number line graph with a closed circle on 30 and shading to the right.
Number line graph with a closed circle on 150 and shading to the right.
Number line graph with a closed circle on 180 and shading to the right.
Answer:
Number line graph with a closed circle on 120 and shading to the right.
Step-by-step explanation:
Because they have collected 30 dollars already and must collect at least 150 dollars, the closed circle would go on 120, going to the right. (150-30=120)
Which expressions represent the total area of the large rectangle.
Answer:
a, c, and e represent the total area
Answer:
(m+n)*6
Step-by-step explanation:
The total area of a rectangle= length*breath
So using this,
Length (l)=n+m
Breath (b)= 6
We know that,
Area of rectangle (A)=l*b
=(n+m)*6
=(n+m)6
I need help getting the answer for this one. Thank you
The next step is to to construct a line through point R is the option;
Place the compass on point T. without changing the setting from the previous step, draw a small arc above [tex]\overleftrightarrow{ST}[/tex]What are the steps to construct a perpendicular to a line?
The steps to construct a perpendicular through the point R are;
Place the compass at point R and draw an arc intersecting the line ST at the point S and T.Place the compass at point S and draw the arc given in the drawing.Place the arc at point T and without changing the setting draw an arc above the line ST to intersect the previous arc.Join the point of intersection of the arcs to the point R to complete the construction of the perpendicular to the line ST passing through RThe step that should be taken next to construct a line through point R that is perpendicular to [tex]\overleftrightarrow{ST}[/tex] is therefore;
Place the compass on point T. without changing the setting from the previous step, draw a small arc above [tex]\overleftrightarrow{ST}[/tex]
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help meh out please:)
The distance between two points is the number of units between them
The distance between the oak tree and the maple tree is 9 yards
How to determine the distance?From the diagram, we have the following highlights:
The distance between the maple tree and the end is [tex]28\frac 26[/tex] yardsThe distance between the oak tree and the end is [tex]11\frac 36 + 7\frac 56[/tex] yardsThe distance (d) between the oak tree and the maple tree is the difference between the above measurements.
So, we have:
[tex]d = 28\frac 26 - (11\frac 36 + 7\frac 56)[/tex]
Simplify the expression in the bracket
[tex]d = 28\frac 26 - (19\frac 26)[/tex]
Subtract
[tex]d = 9[/tex]
Hence, the distance between the oak tree and the maple tree is 9 yards
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The distance between the maple tree and the oak tree is 9 yards
The distance between the maple tree and the end is 28 2 / 6 yards(170 / 6)
The distance between the oak tree to the end is the sum of oak to pine and pine to the end. Therefore,
11 3 / 6 + 7 5 / 669 / 6 + 47 / 6 = 69 + 47 / 6 = 116 / 6 = 58 / 3 yardsTherefore, the distance between the maple tree and the oak tree is as follows;
Difference:Difference is the subtraction of one number from another. Therefore, the distance between the maple tree and the oak tree is the difference between the maple tree to the end and the sum of oak to pine and pine to the end.
170 / 6 - 58 / 3 = 170 - 116/ 6 = 54 / 6 = 18 / 2 = 9 yardsTherefore, the distance between the maple tree and the oak tree is 9 yards
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