For a quadratic function f(x) = ax² + bx + c, we can find the minimum and maximum value using the formula -b/2a or by graphing the function.
We know that the general form of quadratic function is f(x) = ax² + bx + c ; a ≠ 0
The graph of quadratic function is a parabola. The graph is parabola that either opens upward or downward.
For a quadratic function is f(x) = ax² + bx + c,
if a is positive (a > 0) then the parabola opens upward.
In this case you will be finding the minimum value of f(x) at the vertex of parabola.
if a is negative (a < 0), then the parabola opens downward.
In this case you will find its maximum value of f(x) at the vertex of parabola.
Also, the value of -b/2a will tell you the minimum or maximum value of f(x) which is the vertex of the parabola.
Therefore, to find the minimum and maximum of a quadratic function f(x) = ax² + bx + c :
1) find vertex of function from the graph
2) use formula -b/2a
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Write a cubic function with x-intercepts -3/2, 0, 2 and passes through the point (1,3)
write the factors out with reverses signs like this
y = (x+3/2)(x)(x-2)
solve for x = 1
y = -2.5
what can we add to this to get 3
5.5
so
y = (x+3/2)(x)(x-2) + 5.5
at x = 1, y = 3
Hope this helps :)
If you need any more explanation, feel free to ask. If this really helps, consider marking brainliest.
- Jeron
From a hot-air balloon, Justin measures a 34° angle of depression to a landmark
that's 1424 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest hundredth of a foot if
necessary.
The vertical distance of the balloon from the ground will be 960.50 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
From a sight-seeing balloon, Justin estimates a 34° point of sadness to a milestone that is 1424 feet away, estimating on a level plane.
The vertical distance of the balloon from the ground will be given as,
tan 34° = h / 1424
Simplify the equation, then we have
h = 1424 tan 34°
h = 960.50 feet
The upward distance of the inflatable starting from the earliest stage is 960.50 feet.
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Melinda can paint 14 of a wall in the same time that desiree can paint 25 of a wall. How much of a wall will melinda have painted when desiree has finished painting 1 wall?.
Melinda will have painted 56 percentage of a wall for the time taken by Desiree, when she has finished painting 1 wall.
The computation of the difference between the time taken by Desiree and Melinda to paint walls at their respective speeds can be shown using the generalized calculations, as expressed hereunder,
Desiree will take 4x the time for painting 1 wall completely (25x4=100%). Thus, the amount of time taken by Melinda will also be 4x of her actual time, as below,
14×4= 56%
Therefore, Melinda will have covered 56 percent of the wall in the time when Desiree completes painting the entire wall.
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Please help me if I don’t do it I will fail my class
I think that's about right...
Just copy the image down onto your paper
A jar contains 4 blue marbles, 6 red marbles, 10 purple marbles, and 5 green marbles. If you choose one marble, what is the probability that it won't be green?.
Answer: 4/5
Step-by-step explanation:
Let's start with what we know:
4 blue
6 red
10 purple
5 green
So, we have 25 total and 5 green. But we are trying to find the probability it won't be green, in which we have 20 marbles. So the probability it won't be green is 20/25 = 4/5.
What is the only difference between adding and subtracting polynomials?
The basic difference between the addition and subtraction of polynomials has been explained below.
A polynomial is a mathematical expression containing two or more algebraic terms containing variables and their coefficients that involve operations such as addition, subtraction, and multiplication.
The basic difference between the addition and subtraction of polynomials is that since subtraction is the inverse of addition, all terms get the opposite sign upon subtraction. For example -
In addition - 2x²+3x+4 and 3x²+7x+9 are added and we get = 6x²+10x+13
In subtraction - The same polynomials are subtracted = -x²-7x-5
Henceforth, we see that the signs have changed to the opposite.
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Lydia picked some flowers. She said she picked more than 20 flowers, but less than 40 flowers. The number of flowers Lydia picked is a multiple of 3. List at least 3 numbers that could be the number of flowers Lydia picked.
Answer: The numbers of flowers she could have picked are 21, 24, 27, 30, 33, and 36.
Why?: These are all multiples of 3 between 20-40.
Which of the following statements are true?
I. Data sets can only have one mean.
II. Data sets can only have one mode.
III. Data sets can only have one median.
someone help please asap
Answer:
[tex]x= -\sqrt19 -4\\x=\sqrt19-4[/tex]
Decimal version: [tex]x= 8.3589 \\x=0.358899[/tex]
Step-by-step explanation:
1. Move the terms
[tex]x^{2} +10x-2x=5-2[/tex]
2. Collect like terms
[tex]x^{2} +8x=5-2\\x^{2} +8x=3[/tex]
3. Complete the square, you should get
[tex]x^{2} +8x+16=3+16\\(x+4)^{2} =19[/tex]
4. Solve for X
Luis eats 4 pieces of a pizza divided into 6 equal-sized parts.
Omar eats 2 of the pieces.
46+26 models the total amount of pizza Luis and Omar ate.
Which expression is equivalent to 46+26?
CLEAR CHECK
(16+16+16+16)+(16+16)
46+26
(46+46+46+46)+(26+26)
4+6+2+6
Answer:
i think its just 46+26
Step-by-step explanation:
sorry if im wrong
How do you find the domain?
The domain of a function is the set of numbers that can go into a given function.
The set of input values (x) for which a function generates an output value is known as the domain of the function (y).
we can write [tex]y = f(x).[/tex]
domain is the full set of x-values that can be plugged into a function to produce a y-value.
The most effective approach to finding a domain will depend on the type of function.
The domain is expressed using an open bracket or parenthesis, the domain's two endpoints separated by a comma, and then a closed bracket or parenthesis.
To find domain of function we should know the property of that function like what the function can take inside it.
Like if we consider square root function [tex]\sqrt{x}[/tex] so inside root negative numbers are not allowed so value of x should be positive means x>=0
So domain of square root function [0, ∞).
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-4x ≥ 20
8 ≤ -4(x - 1)
3x - 2 > 4 - 3x
Please answer all of them. Please help, I need to get my grade up. No links or I will report. Thank you.
The solutions to the inequalities are x ≤ -5, x ≥ 1 and x > 1
How to determine the solution to the inequalities?From the question, we have the following parameters that can be used in our computation:
-4x ≥ 20
8 ≤ -4(x - 1)
3x - 2 > 4 - 3x
Next, we solve the inequalities
Inequality 1
-4x ≥ 20
Divide both sides of the inequality by -4
So, we have the following representation
x ≤ -5
Inequality 2
8 ≤ -4(x - 1)
Divide both sides of the inequality by -4
So, we have the following representation
-2 ≥ -x - 1
Rewrite as
x + 1 ≥ 2
Evaluate the like terms
x ≥ 1
Inequality 3
3x - 2 > 4 - 3x
Add to both sides of the inequality 3x
So, we have the following representation
6x - 2 > 4
Add to both sides of the inequality 2
So, we have the following representation
6x > 6
Divide by 6
x > 1
Hence, the solution is x > 1
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1)
(2x - 3) + 9 ≥ 3 + 4x
4 3
Answer:
The answer will be x ≤ 3/2
Ayden is 1.55 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 21.15 meters. He stands 16.8 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree to the nearest hundredth of a meter = 7.54 m
What are similar triangles?
If two triangles' corresponding angles and sides are identical and their corresponding sides are proportional, or if the ratios between the lengths of the corresponding sides are comparable, then two triangles are said to be similar.
From the figure,
AB= 21.15 meters
AE = AB - BE = 21.15 - 16.8 = 4.35 meters
BC= height, h
The triangles ABC and ADE are similar triangles
So,
AE/DE = AB/BC
4.35 / 1.55 = 21.15/ h
h = ( 21.15 * 1.55 ) / 4.35
= 32.78/4.35 = 7.54 m
So, the height of the tree to the nearest hundredth of a meter = 7.54 m
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Circle all statements that MUST be true
a. Diagonals of parallelograms bisect each other
b. Parallelograms have four congruent sides
c. Isosceles triangles have 3 congruent angles
d.
If the endpoints of a line segment are equidistant from a third point, that third point lies on the
perpendicular bisector of the line segment.
7. Find the value of X, Y. Show your work
Answer:
6) True, False, False, True;7) x = 135, y = 45.--------------------
Question 6a. Diagonals of parallelograms bisect each other
TRUEb. Parallelograms have four congruent sides
FALSE, it is true for rhombusc. Isosceles triangles have 3 congruent angles
FALSE, it has 2 congruent angles as two sides are congruent.d. If the endpoints of a line segment are equidistant from a third point, that third point lies on the perpendicular bisector of the line segment.
TrueQuestion 7Adjacent angles of a parallelogram are supplementary and opposite angles are congruent.
x + y = 180 and y = 45Find x:
x + 45 = 180x = 180 - 45x = 135To find the unit rate for StartFraction 182 dollars Over 14 feet EndFraction,
a. divide both 182 and 14 by 14.
b. multiply both 182 and 14 by 14.
c. divide both 182 and 14 by 182.
d. multiply both 14 and 182 by 182.
To find the unit rate for Start Fraction 182 dollars Over 14 feet End Fraction,
c. divide both 182 and 14 by 182.
A fraction is a mathematical concept that refers to a component of a whole or, more broadly, any number of equal parts.
An element of the whole is a fraction. The number is shown as a quotient in mathematics, where the numerator and denominator are split.Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction.
Step 1: Divide 182 by 182
182 / 182 = 1
Step 2: Divide 14 by 182
14 / 182 = 0.07660818713450292
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we are asked to test for independence between age (i.e., adult and teen) and drink preferences. the test statistic for this test of independence is
The value of test statistic for test of independence is 62.5
The Chi-square test of independence checks that two variables are related or not. We have to count for two nominal variables. We also believe that the two variables are unrelated. The test allows us to determine whether or not our idea is plausible.
The sections that follow go over what we need for the test, how to perform it, understanding the results, statistical details, and p-values.
Given,
the table shows the beverage preferences for random samples of teens and adults.
For calculating the test statistics,
First wee need to calculate the expected values of every observed values.
Expected values for teens,
[tex]E(50)=\frac{250*400}{1000}=100\\\\E(100=)\frac{250*400}{1000}=100\\\\E(200)=\frac{400*400}{1000}=160\\\\E(50)=\frac{100*400}{1000}=40[/tex]
Expected values for adults,
[tex]E(200)=250-100=150\\\\E(150)=250-100=150\\\\E(200)=400-160=240\\\\E(50)=100-40=60[/tex]
Now, the test statistic is given by:
[tex]X^2=\frac{\sum\limits^n_{i=1}(O_i-E_i)^2}{E_i}[/tex]
Where, Ei=expected value and Oi = observed value
[tex]X^2=\frac{(50-100)^2}{100}+\frac{(100-100)^2}{100}+...\frac{(200-240)^2}{240}+\frac{(50-60)^2}{60}=62.5[/tex]
So, the value of test statistic for this test independence is 62.5.
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Your question is incomplete, here is the complete question
The table below gives beverage preferences for random samples of teens and adults.
teens adults total
coffee 50 200 250
tea 100 150 250
soft drink 200 200 400
other 50 50 100
400 600 1000
we are asked to test for independence between age (i.e., adult and teen) and drink preferences. the test statistic for this test of independence is ?
P is the point (a, a -2) and Q is the point (4-3a, -a).
a
Find the gradient of the line PQ.
b
Find the gradient of a line perpendicular to PQ.
Given that the distance PQ is 10√5, find the two possible values of a.
c
Answer:
[tex]\textsf{a)} \quad \dfrac{1}{2}[/tex]
[tex]\textsf{b)} \quad -2[/tex]
[tex]\textsf{c)} \quad a = -4,\;\; a = 6[/tex]
Step-by-step explanation:
Part (a)[tex]\boxed{\begin{minipage}{9cm}\underline{Gradient Formula}\\\\Gradient $=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Given points:
P = (a, a-2)Q = (4-3a, -a)Substitute the given points into the gradient formula to find the gradient of line PQ:
[tex]\textsf{Gradient}=\dfrac{-a-(a-2)}{(4-3a)-a}=\dfrac{-a-a+2}{4-3a-a}=\dfrac{2-2a}{4-4a}=\dfrac{2(1-a)}{4(1-a)}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Part (b)If two lines are perpendicular to each other, their gradients are negative reciprocals.
Therefore, the gradient of a line perpendicular to PQ is:
[tex]\implies \textsf{Gradient}=-2[/tex]
Part (c)[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Substitute the points and the given distance 10√5 into the formula and solve for a.
[tex]\implies 10\sqrt{5}=\sqrt{((4-3a)-a)^2+(-a-(a-2))^2}[/tex]
[tex]\implies 10\sqrt{5}=\sqrt{(4-3a-a)^2+(-a-a+2)^2}[/tex]
[tex]\implies 10\sqrt{5}=\sqrt{(4-4a)^2+(2-2a)^2}[/tex]
[tex]\implies 500=16-32a+16a^2+4-8a+4a^2[/tex]
[tex]\implies 500=20a^2-40a+20[/tex]
[tex]\implies 25=a^2-2a+1[/tex]
[tex]\implies a^2-2a-24=0[/tex]
[tex]\implies a^2-6a+4a-24=0[/tex]
[tex]\implies a(a-6)+4(a-6)=0[/tex]
[tex]\implies (a+4)(a-6)=0[/tex]
Apply the zero-product property:
[tex]\implies a+4=0 \implies a=-4[/tex]
[tex]\implies a-6=0 \implies a=6[/tex]
Therefore, the two possible values of a are:
a = -4, a = 6Please help !!!!!!!!! Meeee
Answer:
B: 25
Step-by-step explanation:
We want to find 1875/75. 1875=1800+75
So, 1875/75=(1800+75)/75=24+1=25
which racing organization saw its television ratings increase 28% over 2021 to a season average of 1.2 million viewers?
Formula 1 (F1) is the racing organization which saw its television rating increase 28% over 2021 to a season average of 1.2milion viewers.
Formula 1 (F1) season US Television viewership records,season race audience average is 1.21 million up 28% over record sets in 2021.Formula 1 (F1) breaks record for tv audience size in USA,Twelve of 22 races set in USA in which race more females and youngers viewers,As television viewership record fell by the wayside all year in 2022 the formula 1 world championship season ended as the most viewed over USA television,in addition more females and youngers viewers F1 races on USA television than ever before.
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Where is the function increasing?
The function increases when x > 0
The function increases when x > 1
The function increases when x > 2
The function increases when x > -3
According to the given image, the given function is increasing at (C) x > 2.
What are functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The relationship between the input or domain and the output or range is known as the function rule.
If and only if there is a single value in the range for each domain value, a relation is a function.
A function is denoted by the notation f x, where x is the input value.
A function has the general form y = f x.
So, let's consider the given image:
The function is increased from the point +2 on the x-axis.
Which can be the point x > 2.
Therefore, according to the given image, the given function is increasing at (C) x > 2.
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Complete question:
Where is the function increasing?
a. The function increases when x > 0
b. The function increases when x > 1
c. The function increases when x > 2
d. The function increases when x > -3
please helpFill in the blank with the correct response.
if 9/24 = 3/i then i =_______
Answer:
Step-by-step explanation:
[tex]\frac{9}{24} = \frac{3}{i} \\9i = 72\\i = 8[/tex]
∴ i is 8.
!Help! Can someone help me solve for the variables?
I know the sum is 360 but i don't know where to start.
The measure of a° is 144°.
The measure of b° is 67°.
What is a trapezium?A trapezium is a quadrilateral where 1 pair of sides are parallel and the sum of angle pairs between parallel lines is 180 degrees.
We have,
Two parallel lines.
The sum of the angle pairs between parallel lines = 180°
This means,
a + 36 = 180
a = 180 - 36
a = 144
b + 113 = 180
b = 180 - 113
b = 67
Thus,
The value of a° is 144°.
The value of b° is 67°.
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Micah is perparing for a piano recital . He practices for 50 minutes on Monday and 90 minutes on Wendnesday.
Micah increased his practice time by 80%.
What is percent?
A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.
Given:
Micah is preparing for a piano recital .
He practices for 50 minutes on Monday and 90 minutes on Wednesday.
Micah increased his practice time by 40%.
%increase = (Final value - starting value) / |starting value| x 100
= (90 - 50) / |50| x 100
= 40/50 x 100
%increase = 80%
Hence, Micah increased his practice time by 80%.
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Complete question:
Seven friends are buying tickets to a concert. Each person pays $8. How much money do they pay altogether?
$
Answer:
56$
Step-by-step explanation:
8$x7=56.
you just need to multiply it
you are solving a measurement problem where the numbers 5.07 x 109 and 1.087 x 10−4 are divided. how many significant digits should the quotient have?
The division of the two numbers in scientific notation 5.07 × 10⁹ ÷ 1.087 × 10⁻⁴ is 4.664 × 10¹³
Scientific NotationScientific notation is a means in which we use to represent numbers based on a standard measure.
In this problem, we have to perform a mathematical operation with two numbers expressed in scientific notation.
To divide 5.07 × 10⁹ by 1.087 × 10⁻⁴;
We need to divide 5.07 by 1.087
The result given is 5.07 ÷ 1.087 = 4.664
The second step is to note that when 10⁹ ÷ 10⁻⁴,
Using law of indices, it becomes 10⁹ ÷ 10⁻⁴ = 10⁽⁹⁺⁴⁾ = 10¹³
We can now rewrite our answer as
5.07 × 10⁹ ÷ 1.087 × 10⁻⁴ = 4.664 × 10¹³
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Help with question 14
Answer:
Step-by-step explanation: I think its the second one
need help fast what is the equation
The equation is 128 + 2x = 180.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The sum of the same-side interior angles between two parallel lines is supplementary
This means,
128 + 2x = 180
2x = 180 - 128
2x = 52
x = 26
Thus,
The value of x is 26.
The equation is 128 + 2x = 180.
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Helpppppppppppppppppppppppp
Answer:
Christianity bc its the earliest for everything
(-1,-10)(−1,−10)left parenthesis, minus, 1, comma, minus, 10, right parenthesis and (5,2)(5,2)left parenthesis, 5, comma, 2, right parenthesis.
Answer: 4
Step-by-step explanation:
-1+-10 is -11
5+2 is 7
-11+7 is 4