Answer:
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
f(x) = x² - X + 2.
Quadratic equation with [tex]a = 1, b = -1, c = 2[/tex]
So
[tex]\Delta = b^2-4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]
[tex]x_{v} = -\frac{(-1)}{2} = \frac{1}{2}[/tex]
[tex]y_{v} = -\frac{-7}{4} = \frac{7}{4}[/tex]
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Right triangle ABC is shown.
Triangle A B C is shown. Angle A C B is a right angle and angle C B A is 50 degrees. The length of A C is 3 meters, the length of C B is a, and the length of hypotenuse A B is c.
Which equation can be used to solve for c?
sin(50o) = StartFraction 3 Over c EndFraction
sin(50o) = StartFraction c Over 3 EndFraction
cos(50o) = StartFraction c Over 3 EndFraction
cos(50o) =
Answer:
A and A.
Step-by-step explanation:
Got it correct on edge 2022.
Perimeter of a 14cm,10cm,6cm and 20cm shape?
Answer:
The perimeter is 50 cm.
Step-by-step explanation:
P= 14 + 10 + 6 + 20= 50 cm
please answer i will mark brainliest :)
Answer:
c I think that's the right answer
Oakley babysits on weekends. He charges a flat fee of $12, plus an additional $5 for each hour that he babysits. How much money would Oakely make if he babysits for 4 hours?
Answer:
32
Since theres a flat fee he automatically starts at 12 since he gets 5 every hour for 4 hours (5×4) ending up at 20. You add the total and the flat fee 20+12= 32
Answer:
$32
Step-by-step explanation:
First you must set up the equation.
A flat fee of $12 means it will be added and $5 each hour for 4 hours so 5 will be multiplied by 4.
$12 + $5 * 4
12 + 5 * 4 (or 12 + (5 * 4), whatever makes you remember it better)
Remember PEMDAS (Parentheses, Exponents, Multiplication, Divisiom, Addition, Subtraction)
Multiplication comes before Addition so you get 12 + 20
12 + 20 = 32
Remember to put units, so you would get $32.
A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the test statistic to decide whether the mean transaction time exceeds 60 seconds.
a. 1.457
b. 2.333
c. 1.848
d. 2.037
Answer:
b. 2.333
Step-by-step explanation:
Test if the mean transaction time exceeds 60 seconds.
At the null hypothesis, we test if the mean transaction time is of 60 seconds, that is:
[tex]H_0: \mu = 60[/tex]
At the alternate hypothesis, we test if it exceeds, that is:
[tex]H_1: \mu > 60[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
60 is tested at the null hypothesis:
This means that [tex]\mu = 60[/tex]
A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds.
This means that [tex]n = 16, X = 67, s = 12[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{67 - 60}{\frac{12}{\sqrt{16}}}[/tex]
[tex]t = \frac{7}{3}[/tex]
[tex]t = 2.333[/tex]
Thus, the correct answer is given by option b.
Factor this polynomial.
.-2x2 - 7x-3
Answer:
Its B
Step-by-step explanation:
Mark as Brainllest!!
Complete the table of ordered pairs for the linear y=2x-8
Given:
Consider the below figure attached with this question.
The linear equation is:
[tex]y=2x-8[/tex]
To find:
The values to complete the table of ordered pairs for the given linear equation.
Solution:
We have,
[tex]y=2x-8[/tex]
Substituting [tex]x=0[/tex] in the given equation, we get
[tex]y=2(0)-8[/tex]
[tex]y=0-8[/tex]
[tex]y=-8[/tex]
So, the value for first blank is -8.
Substituting [tex]y=-2[/tex] in the given equation, we get
[tex]-2=2x-8[/tex]
[tex]-2+8=2x[/tex]
[tex]\dfrac{6}{2}=x[/tex]
[tex]3=x[/tex]
So, the value for second blank is 3.
Substituting [tex]x=2[/tex] in the given equation, we get
[tex]y=2(2)-8[/tex]
[tex]y=4-8[/tex]
[tex]y=-4[/tex]
So, the value for third blank is -4.
Therefore, the required complete table is:
x y
0 -8
3 -2
2 -4
carol and jada sold raffle tickets to raise money for a new playground carol sold 2045 tickets jada sold 356 more than carol how many did jada sell
What happens if you try to use L'Hopital's Rule to find the limit?
lim x/√x^2 +6
x→[infinity]
Required:
a. You cannot apply L'Hopital's Rule because the function is not differentiable.
b. You cannot apply L'Hopital's Rule because the numerator equals zero for some value x = a.
c. You cannot apply L'Hopital's Rule because the function is not continuous.
d. You cannot apply L'Hopital's Rule because the denominator equals zero for some value x = a.
e. Repeated applications of L'Hopital Rule result in the original limit or the limit of the reciprocal of the function.
If we try to use L'Hopital's Rule to find the limit we cannot apply L’Hopital’s Rule because the denominator equals zero for some value x = a, the correct option is D.
We are given that;
Function [tex]x/√x^2 +6[/tex]
Now,
The limit of the function as x approaches infinity is an indeterminate form of type ∞/∞.
However, L’Hopital’s Rule can only be applied when the limit is in the form 0/0 or ∞/∞.
So, L’Hopital’s Rule cannot be applied in this case
Therefore, by L’Hopital’s rule answer will be You cannot apply L’Hopital’s Rule because the denominator equals zero for some value x = a.
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i need the answer of this with steps and solutions fast plz
Answer:
[tex] 1 \dfrac{13}{15} [/tex]
Step-by-step explanation:
[tex] 2 \dfrac{1}{5} - \dfrac{1}{3} = [/tex]
[tex] = \dfrac{11}{5} - \dfrac{1}{3} [/tex]
[tex] = \dfrac{33}{15} - \dfrac{5}{15} [/tex]
[tex] = \dfrac{28}{15} [/tex]
[tex] = 1 \dfrac{13}{15} [/tex]
Find each missing length to the nearest tenth.
[tex]\huge\bold{Given:}[/tex]
Length of the perpendicular = 7
Length of the base = 10
[tex]\huge\bold{To\:find:}[/tex]
The length of the missing side (hypotenuse).
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\purple{x\:=\: 12.21}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
Let the length of the missing side be [tex]x[/tex].
Using Pythagoras theorem, we have
(Hypotenuse)² = (Perpendicular)² + (Base)²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = (7)² + (10)²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 49 + 100
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 149
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex]\sqrt{149}[/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = 12.206
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = 12.21.
Therefore, the length of the missing side [tex]x[/tex] is [tex]12.21[/tex].
[tex]\huge\bold{To\:verify :}[/tex]
[tex]\longrightarrow{\green{}}[/tex] (12.21)² = (7)² + (10)²
[tex]\longrightarrow{\green{}}[/tex] 149 = 49 + 100
[tex]\longrightarrow{\green{}}[/tex] 149 = 149
[tex]\longrightarrow{\green{}}[/tex] L.H.S. = R. H. S.
Hence verified.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
Can anyone explain "Predicting Results of Rigid Transformations"?
Answer: Rigid just means that the whole shape goes through the same transformation, so with rotations, reflections, and translations, the shape should not change at all, just in a different place or orientation.
In a translation, ALL of the points move the same distance in the same direction. A translation is called a rigid transformation or isometry because the image is the same size and shape as the pre-image. ... In addition, the corresponding segment sides of the pre-image and image are parallel.
A rigid transformation preserves both the side lengths and the angle measures of a polygon. Step-by-step explanation: Rigid transformations are the transformations which does not affect the size and the shape of figure . The figure doesn't shrink or get enlarger.
There are three different types of transformations: translation, reflection, and rotation.
The distance from each point in the figure to the center of rotation is preserved. A rigid transformation is a transformation that preserves congruence.
More information for Rigid
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[tex]\color{yellow}{}[/tex]
Review the graph of complex number z. On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (negative 3, 1). What is the modulus of z?
Edge
Answer:
The modulus of z is [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Complex number:
A complex number, given by:
[tex]z = x + iy[/tex]
Can be represented also as a point (x,y).
The modulus is given by:
[tex]|z| = \sqrt{x^2 + y^2}[/tex]
Point z is at (negative 3, 1). What is the modulus of z?
[tex]x = -3, y = 1[/tex]. So
[tex]|z| = \sqrt{x^2 + y^2} = \sqrt{(-3)^2+1^2} = \sqrt{10}[/tex]
The modulus of z is [tex]\sqrt{10}[/tex]
Answer:
-2
Step-by-step explanation:
if this is the right problem it is -2
The list price on slacks is $22, and the list price on jumpers is $37. If Petit’s Clothing Store orders 30 pairs of slacks and 40 jumpers at a discount rate of 11%, what is the trade discount on the purchase?
Answer: $235.4
Step-by-step explanation:
Given
Price list on slacks is $22
Price list on jumpers is $37
Store ordered 30 pairs of slacks and 40 Jumpers
Total price becomes
[tex]\Rightarrow 22\times 30+37\times 40\\\Rightarrow \$2140[/tex]
for a discount of 11%
Trade discount is [tex]2140\times 11\%[/tex]
[tex]\Rightarrow 2140\times 0.11\\\Rightarrow \$235.4[/tex]
2 3 12 13 52 53 what number comes next
In function notation, f(x) is another way of saying ______.
1.)y
2.)x
3.)or none of the above
Answer:
y
Step-by-step explanation:
In function notation, f(x) is another way of saying y. Then the correct option is A.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
Tables, symbols, and graphs can all be used to represent functions. Every one of these interpretations has benefits. Tables provide the functional values of certain inputs in an explicit manner. How to compute direct proportionality is succinctly stated in symbolic representation.
The function is represented as,
y = f(x)
In function notation, f(x) is another way of saying y. Then the correct option is A.
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PLEASE I NEED THE CORRECT ANSWER ILL GIVE BRAINLISET 100 students are interviewed to see which of biology, chemistry or physics they prefer.
22 of the students are girls. 6 of the girls like biology best.
23 of the boys prefer physics.
14 out of the 32 who prefer chemistry are girls.
What percentage of the students prefer biology?
..........................................................
Select all the expressions that are equivalent to 13 - x *
You gave no options but the simplest way to solve this is to set it equal to all of the answers to see if it is correct.
Use the graph to estimate f(4)
Answer:
f(4) = 1
Step-by-step explanation:
Locate x = 4 on the x- axis, then go vertically up to meet the graph at (4, 1 ) , then
f(4) = 1
The value of the function f(4) is 1. The correct option is C.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The value of the function f(4) will be calculated as below:-
Locate x = 4 on the x- axis, then go vertically up to meet the graph at (4, 1 ) ,
f(4) = 1
Therefore, the value of the function f(4) is 1. The correct option is C.
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Find the value of x for which a || b.
Answer:
x = 35
Step-by-step explanation:
x and 3x+40 are same side interior angles and same side interior angles are supplementary when the lines are parallel
x + 3x+40 = 180
Combine like terms
4x+40 =180
4x = 180-40
4x = 140
Divide by 4
4x/4 = 140/4
x = 35
Answer and Step-by-step explanation:
To solve for x, we add together the angles, and equal it to 180.
This is because the angles shown are same side interior angles, and add up to 180 degrees.
x + 3x + 40 = 180
Subtract 40 and combine like terms.
4x = 140
Divide 4 from both sides of the equation.
x = [tex]35[/tex]
The value of x is 35.
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Dertemine a área total at
Question
At a certain university, intramural volleyball is chosen as an activity by 50% of the student population. How likely is it that a
randomly chosen student will or will not participate in intramural volleyball?
Answer:
50%
Step-by-step explanation:
50% of the student population chooses instramural volleyball, meaning 50% doesn't. So if a random student is chosen, then it is a 50% chance that they will choose volleyball and 50% chance they won't.
Illustrative Example 1:
The grades in Statistics of 10 students are 87, 84, 85, 85, 86, 90, 79, 82, 78, 76.
What is the mode?
Given:
The data set is:
87, 84, 85, 85, 86, 90, 79, 82, 78, 76
To find:
The mode of the given data set.
Solution:
We have,
87, 84, 85, 85, 86, 90, 79, 82, 78, 76
Arrange the data values in the ascending order.
76, 78, 79, 82, 84, 85, 85, 86, 87, 90
We know that the mode of date set is the most frequency value of the data set.
From the above data set it is clear that the number 85 has the highest frequency 2.
Therefore, the mode of the data set is 85.
The radius of a cylindrical water tank is 4.5 ft, and its height is 10 ft. What is the volume of the tank?
Answer:
636.3 cubic meters
Step-by-step explanation:
Volume of cylinder= pi × radius² × height
3.142 × 20.25 × 10 = 636.255 rounded to the nearest one decimal place is 636.3
Have a nice day.
11. f(x) = 4x4 - x2 + 9. Find f(-4).
Answer:
f ( -4 ) = 1024 + 8 + 9
Step-by-step explanation:
f ( x ) = 4x⁴ - x² + 9
If f ( - 4 ) then we get
f ( -4 ) = 4 ( -4)⁴ - ( - 4)² + 9
Expand the exponents
f ( - 4 ) = 4 ( 256 ) + 8 + 9
multiply the numbers
f ( -4 ) = 1024 + 8 + 9
What's the answer to this? and please explain.
===========================================================
Use this formula
a & b/c = (a*c+b)/c
to convert from a mixed number to an improper fraction
So,
a & b/c = (a*c+b)/c
3 & 3/4 = (3*4+3)/4
3 & 3/4 = 15/4
---------------------------------------------------
Next, we add the fractions 15/4 and 5/6. The denominators aren't the same, so we can't add right away. We need to get the denominators to the LCD.
In this case, the LCD is 4*6 = 24
The fraction 15/4 becomes 90/24 after multiplying top and bottom by 6.The fraction 5/6 becomes 20/24 after multiplying top and bottom by 4Now we can add the fractions:
90/24+20/24 = (90+20)/24 = 110/24
---------------------------------------------------
So far, we've added the 3&3/4 portion to the 5/6 portion to get the result 110/24
The last thing to do is to add on the two 1/3 ft pieces, which means we're adding on 2/3 of a foot
2/3 = 16/24 after multiplying top and bottom by 8
Add this to the result of the last section
110/24+16/24 = (110+16)/24 = 126/24
---------------------------------------------------
From here, we convert the improper fraction 126/24 to decimal form
Using a calculator, you should find that 126/24 = 5.25
The result is larger than 5, which means she used too much ribbon. There won't be enough ribbon to do everything she wants to do.
---------------------------------------------------
The shortcut we can take is to type the following into the calculator
3+3/4+5/6+2/3
doing so should lead to 5.25
Answer:
Yes
Step-by-step explanation:
So at the begining, Cherly has 60 in (12inx5ft) of ribbon. She uses 45 in(3.75x12) to make the hair bow, leaving 15 in of ribbon. She, then, uses 10 in (5/6x12) of ribbon, leaving 5 in. After that, Cheryl uses 8 in [2(1/3x12)] to put on the picture frame, leaving two inches of ribbon.
A, B , and C are collinear points: B is between A and C. If AB = 36, BC = 5x - 9 , and AC = 54 , find x
9514 1404 393
Answer:
x = 5.4
Step-by-step explanation:
The segment sum theorem tells you ...
AB +BC = AC
36 +(5x -9) = 54
5x = 27 . . . . . . . . . . . subtract 27 from both sides
x = 5.4 . . . . . . . . . . divide by 5
HELP ANYONE OUT THERE WITH MY MATH
Answer:
x is 37.,.,.,.,.,.,.,.,.,.,.,.,.,.,.,.
Answer:
x = 37
Step-by-step explanation:
Interior angles of a square is 90 each.
∠JKL = 90°
Given ∠JKL = 3x - 21
Therefore, 3x - 21 = 90
3x = 90 + 21
3x = 111
x = 37
Create a system of equations whose solution is (2,-4).
Answer:
x=-4 and y=2 Those 2 equations when graphed give a vertical line and a horizontal line that intersect at the point (-4,2)
x+4=0 and y-2=0 are the same two lines.
or if you want more complicated systems of equations, with the same solution:
x+y=-2 and x-y=-6
in standard form, that's y=-x-2 and y=x+6 Graph those two lines and they intersect at (-4,2)
Those 2 lines are with slopes of -1 and +1. Those 2 equations are a system of equations
whose solution is x=-4 and y=2.
Rotate two perpendicular lines around the point (-4,2) and you get more systems of
equations with the same solution.
They don't have to be perpendicular though. x+y=-2 and x=-4 are two lines forming
a 45 degree angle, with the same solution (-4,2)
They don't have to be linear either. Take a parabola with the vertex (-4,2) and the line x=-4.
They intersect at the point (-4,2). That parabola could be the simple y=x2 shifted up and
to the left, to y-2 = (x+4)2 or y=x2+8x+18 or it could be any one of a family of parabolas with
the same vertex.
You could have 2 circles tangent at the point (-4,2) Endless circles could have that point
as a tangent and their equations having that same solution (-4,2)
Step-by-step explanation:
Hope this helps <3