The vertex is (3,16) and the quadratic equation in vertex form is [tex]f(x)=(x-3)^{2}+16\\[/tex].
What is quadratic equation?Any equation in algebra that can be put into standard form is called a quadratic equation (from the Latin quadratus, which means "square").
As well as being referred to as the roots or zeros of the expression on the left-hand side of the equation, the values of x that satisfy it are known as solutions of the equation. There are only two possible answers to a quadratic equation. A double root is said to exist if there is only one solution. In the case where all of the coefficients are real values, there are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or all three of the aforementioned options. If complex roots are taken into account, then a quadratic equation will always have two roots, with a double root counting as one. An equivalent equation can be created from a quadratic equation.
Calculations:
[tex]f(x)=x^{2} -6x+25\\ = x^{2} -2.x.3+(3^{2} )-(3^{2} )+25\\=(x-3)^{2} -9+25\\=(x-3)^{2}+16\\[/tex]
Comparing this from the vertex, y=[tex]a[/tex][tex](h-x)^{2} +k\\[/tex]
h=3 and k=16
Hence, vertex is (3,16).
[tex]f(x)=(x-3)^{2}+16\\[/tex]
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What is the quotient of 80 divided by 2/3
Answer:
approximately 13.333333....
Step-by-step explanation:
2/3=0.66666...
80/0.66666...=13.333333..
P = 2 ( l + w ) explain how to work this out please
Answer:
2l + 2w
Step-by-step explanation:
using the distributive property
a(b + c) = ab + ac
2(l + w)
= 2l + 2w
Which is the angle measured in a horizontal circle around your horizon? ecliptic equator azimuth right ascension
Azimuth is the angle measured in a horizontal circle around your horizon.
In this question,
The horizon angle is the maximum upwind slope in wind exposure / sheltering studies.
A line from the center of the Earth which continues through the observer's body and the top of the observer's head. This line is zenith.
Azimuth is the coordinate direction that runs parallel to the horizon and rotates clockwise from north (0 degrees) to east (90 degrees) to south (180 degrees) to west (270 degrees) back to north (360 degrees).
The meridian is an imaginary North-South line running through the zenith.
Therefore, Azimuth is the angle measured in a horizontal circle around your horizon.
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pls help marking brainliest pic attached
Answer:
4
Step-by-step explanation:
16x4=64
Answer:
4 chapters
Step-by-step explanation:
If Raj can read 1 chapter in 16 minutes you need to figure out how many times 16 goes into 64. Divide 64 by 16 and you get 4. Which means Raj can read 4 chapters in 64 minutes.
Large numbers are those numbers that have a bigger value than the numbers that we use in daily life. such numbers tend to create a sense of fear among children and they often skip solving problems that have large numbers in them. for example, 1 million, 1 billion, etc., are large numbers that are used either to show the population of a country or express large amounts of money in a bank account.
These periods are named as ones, thousands, lakhs, and so on. The one's period consists of the first three digits of the large number, starting from the right.
Everyone learns how to count numbers at a very young age starting from a single digit up to seven digits. This is done with the help of the place value system.
While writing large numbers, we always keep the place value system in mind to ensure that it is written correctly. According to the Indian place-value system, when a number is written in the standard form, each group of digits separated by a comma is called a period.
These periods are named as ones, thousands, lakhs, and so on. The one's period consists of the first three digits of the large number, starting from the right. The thousands period consists of the next two digits. The lakhs period consists of the next two digits and it continues.
Some other large numbers are read and written as follows:
1,000,000,000 = one billion
1,000,000,000,000 = one thousand billion
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a radioactive substance decays exponentially. a scientist begins with 180 milligrams of a radioactive substance. after 33 hours, 90 mg of the substance remains. how many milligrams will remain after 43 hours?
The required weight after 43 hours is 72. 96mg
How to determine the valueFrom the information given, we have that;
A Scientist begins with 180 milligrams of a radioactive substance
Let us take Po = 180 milligrams
Using the expression;
[tex]P(t) = Poe^k^t[/tex]
Substituting the values of t = 33, P = 90mg and Po = 180
90 = 180e^33t
[tex]e^3^3^t = \frac{1}{2}[/tex]
Take the log of both sides
[tex]33ln(e^k) = ln (\frac{1}{2} )[/tex]
[tex]k = -\frac{ln 2}{33}[/tex]
k = - 0. 0210
The equation becomes: P(t) = 150e^-0.0210
Substitute t as 43
[tex]P(43) = 180e^-^0^.^0^2^1^0 ^*^4^3[/tex]
P(43) = 72. 96 mg
Hence, 72. 96 mg will remain after 43 hours.
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Does the figure below appear to have line symmetry? If so, how many lines of symmetry?
Answer:
Yes
Step-by-step explanation:
Wouldn't there be 3? because lines of symmetry is basically two lines that look the same and are the same. so the points on the end counts as 2 since it's on opposite side, and the two lines in middle count as 1. So I am going with 3 symmetrical lines amount.
april needs to rent a car while on vacation. the rental company charges $18.95, plus 16 cents for each mile driven. of april only has $40 to spend on the car rental, what is the maximum number of miles she can drive?
Answer:
Step-by-step explanation:
18.95+.16 = 19.11
answer is 2 miles is the maximum
6. Розв'яжіть систему рівнянь способом додавання
79
Відповідь:
3x + 4y = -1,
-3x + 7y = 23.
Відповідь:
Answer:
x= -85/33 ; y=2
Step-by-step explanation:
The simultaneous equation first when we add the y vale become 2, y=2 then to get x value the first equation multipled by -7 & the second equation by 4 the we will gate x=-85/33
-5x divided by 2 >37
Answer: x < -14.8
Step-by-step explanation:
To solve for x, we will isolate the x-variable.
Given:
[tex]\frac{-5x}{2}[/tex] > 37
Multiply both sides of the equation by 2:
-5x > 74
Divide both sides of the equation by -5:
➜ Since we are dividing by a negative, we will flip the direction of the sign.
x < -14.8
converse of if a triangle has either two equal sides or two equal angles, then it is an isosceles triangle
It is an isosceles triangle if a triangle has either two equal sides or two equal angles,
What is converse of a statement?The converse of a statement is formed by switching the hypothesis and the conclusion.
Given the statement 'if a triangle has either two equal sides or two equal angles, then it is an isosceles triangle'
Hypothesis - if a triangle has either two equal sides or two equal angles, Conclusion - then it is an isosceles triangle
The converse will be created by switching the hypothesis with conclusion and vice versa to have ' It is an isosceles triangle if a triangle has either two equal sides or two equal angles,
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(8x-9y=-13
(2x-3y = -7
Answer:
the answer is x=17,y=14/3
Answer:
x=4 y=5
Step-by-step explanation:
8x-9y=-13
2x-3y=-7
Solve for y:
Multiply the bottom by 4 to have the x's equal each other and cancel out:
8x-9y=-13
8x-12y=-28
Then subtract:
0x+3y=15
y=15/3 -> y=5
Solve for x:
Multiply the bottom by 3 to have the y's equal each other and cancel out:
8x-9y=-13
6x-9y=-21
Then subtract:
2x=8
x=4
What are the possible values of x for the following functions?
f(x)=2-x/x(x-1)
Answer:
fx 2
gy
jjhuffff
vct5
yguutfufyhdyts, us f Rd dgidtetdigdeieot
Simplify by combining like terms.
3x^2y^2 + 4xy - 2x^2y^2 - 6xy
Hello,
3x²y² + 4xy - 2x²y² - 6xy = x²y² -2xy
A soccer ball was kicked toward the goal. the horizontal component of velocity was 22 m/s and the vertical component was 12 m/s . what is the magnitude of the resultant velocity of the soccer ball?
The magnitude of the resultant velocity of the soccer ball is 25.06 m/s .
Let the horizontal component of velocity be [tex]V_{x}[/tex] and the vertical component of velocity be [tex]V_{y}[/tex].
The magnitude of the resultant velocity will be represented by V.
So, we can write
The horizontal component of velocity = [tex]V_{x}[/tex] = 22 m/s
The vertical component of velocity = [tex]V_{y}[/tex] = 12 m/s
The relation between horizontal component, vertical component and resultant velocity is,
[tex]V^{2} = V_{x} ^{2} + V_{y} ^{2}[/tex]
On substituting value of horizontal component and vertical component, we get
[tex]V^{2}[/tex] = [tex](22)^{2} + (12)^{2}[/tex]
[tex]V^{2}[/tex] = 484 + 144
[tex]V^{2}[/tex] = 628
V = [tex]\sqrt{628}[/tex]
V = 25.06 m/s
The magnitude of the resultant velocity of the soccer ball is 25.06 m/s .
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let and let be a vector with length that starts at the origin and rotates in the -plane. find the maximum and minimum values of the length of the vector . in what direction does point?
The length of the vector u*v has a maximum value of 16 and a minimum value of 0, and it is moving in a positive z-direction.
What is the maximum and minimum values of the length of the vector? in what direction does point?Generally, the equation for is mathematically given as
Consider the following vector:
[tex]\begin{aligned}\mathbf{v} &=0 \mathbf{i}+4 \mathbf{j}+0 \mathbf{k} \\&=\langle 0,4,0\}\end{aligned}[/tex]
Let us assume that u is a vector that has a length of four, that begins at the origin, and rotates in the x-y plane.
This vector creates a circle with the origin serving as the circle's center and a radius of 4.
So, the coordinates of u can be taken as,
[tex]u=(x\pm \sqrt{4^2-x^2 ,0})[/tex]
Here, 0 [tex]\leq[/tex]x [tex]\leq[/tex] 4.
Now, the cross product of the two vectors u and v is,
[tex]\begin{array}{ccc}\mathbf{i} & \mathbf{j} & \mathbf{k} \\x & \pm \sqrt{4-x^2} & 0 \\0 & 4 & 0\end{array}[/tex]
[tex]&=\mathbf{i}(0-0)-\mathbf{j}(0-0)+\mathbf{k}(4 x-0) \\&=4 x \mathbf{k}\end{aligned}[/tex]
The length of the vector u* v is,
[tex]\begin{aligned}|\mathbf{u} \times \mathbf{v}| &=\sqrt{(4 x)^2} \\&=4 x\end{aligned}[/tex]
Here, 0 <=x <= 4.
If x=4, then u*v is,
[tex]\begin{aligned}\mathbf{u} \times \mathbf{v}| &=4 \times 4 \\&=16 \\|\mathbf{u} \times \mathbf{v}| &=4 \times 0 \\&=0\end{aligned}[/tex]
In conclusion, As a result, the length of the vector u*v has a maximum value of 16 and a minimum value of 0, and it is moving in a positive z-direction.
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CQ
Let v = 4j and let u be a vector with length 4 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector u
The point (-6,-5) across y=-x
Answer:
(5, 6 )
Step-by-step explanation:
under a reflection in the line y = - x
a point (x, y ) → (- y, - x ) , then
(- 6, - 5 ) → (5, 6 )
Multiply numbers with decimals
2.34 x 1.6
Answer:
3.744
Step-by-step explanation:
2.34
* 1.6
-------
1404
+
234
---------
3.744
In the expression -3 which is the correct order in which operations have been done to x?
5
(1) x was divided by 5 and the result was subtracted from 3.
(2) x had 3 subtracted from it and the result was then divided by 5.
(3) x was divided by 5 and 3 was subtracted from the result.
(4) 5 was divided by x and then 3 was subtracted from the result.
Choose an expression for the input-output table. Next, using a variable for the value in the input column, determine the next two values in the table if the table were followed.
Option a, 2x + 1, 6 and 13, 7 and 15.
Here, we are given input-output table as shown in the figure.
To find the equation for this table let us look at each option one by one-
a. 2x + 1
Here if we take input x = 2
output = 2(2) + 1
= 5
If x = 3
output = 7
and if we check for other values also, 2x + 1 will satisfy.
Thus, 2x + 1 is the correct equation.
we can check the points as well-
if x = 6
output = 2(6) + 1 = 13
and if x = 7
output = 2(7) + 1
= 15
Since, we've found the correct answer in option a, we do not need to check the other options.
Thus, option a is the correct answer.
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13 and 9 please help
Answer:
x>-4, x<=27.5
Step-by-step explanation:
First mark your digits on the number line. For question 9, it seems that x>-4, so mark that on your number line and draw an empty circle with an arrow pointing right.
For 13 multiply both sides by 5/4, and your answer is 27.5>=w. Mark it down with a filled in circle and an arrow going to the left.
In Exercises 31−34, tell whether the data in the table can be modeled by a linear equation. Explain. If possible, write a linear equation that represents y as a function of x. Help with 34 ; please include a explanation. Thanks
The slope across the values of the table are not the same, therefore, the table cannot be modelled by a linear equation.
How to Determine a Linear Equation Table?If a table can be represented by a linear equation, then the slope/rate of change between every two pairs of values on the table must be the same. If it's not, then it is not a linear equation that represents y as a function of x.
Slope/rate of change between (1, 18) and (2, 15):
Slope = 18 - 15/1 - 2
Slope =-3
Slope/rate of change between (2, 15) and (8, 9):
Slope = 15 - 9 / 2 - 8
Slope = 6/-6 =
Slope = -1
Therefore, the slope across the values of the table are not the same, therefore, the table cannot be modelled by a linear equation.
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What is the equation and the total amount? last one for this topic
w=28t+600
908 liters
here you go :)
Name a Linear Pair.
Answer:
MSN < LSO
Step-by-step explanation:
Identical Shapes which makes them linear pairs because they pair with each other.
Thanks Please Mark Brainliest, (Trying to rank to genius)
Geometry B.5 Add
Learn with an example
If TU = 14 and UV = 10, what is TV?
5
Drag and drop the correct answer choice to each answer blank.
The length of four rivers in Africa is shown in the table below.
River Length (feet)
Nile 21,800,000
Congo 15,010,000
Ubangi 3,520,000
Zambezi 83,800,000
How is the length of the Zambezi river written in scientific notation?
Answer:
8.38 × 10^7
Step-by-step explanation:
first digit of number X 10 raised to however many digits are after the first
The solution is Option D.
The length of the Zambezi river written in scientific notation is
L = 8.38 x 10⁷ feet
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
The length of the Zambezi river in feet L = 83,800,000 feet
Now , the scientific notation is given by in powers of 10
So ,
The value of L in scientific notation is given by
The value of L = 838 x 10⁵ feet
The value of L = 8.38 x 10² x 10⁵ feet
So , on simplifying the equation , we get
The value of L = 8.38 x 10⁷ feet
Therefore , the value of L is 8.38 x 10⁷ feet
Hence , The length of the Zambezi river written in scientific notation is
L = 8.38 x 10⁷ feet
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5=5/ax+1
Help?? I need to find the value of x. I don’t have the value of a
The value of a is zero from the given expression
Subject of formulaSubject of formula is a way of representing a variable with another variable.
Given the expression below;
5=5/ax+1
We are to make x the subject of the formula
1 =1/ax+1
Cross multiply
ax+1 = 1
ax = 1-1
ax = 0
Find the value of a
a = 0/x
a = 0
Hence the value of a is zero from the given expression
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Find the inequality represented by the graph.
Answer:
[tex]y\le -\frac{1}{3}x + 1[/tex]
Step-by-step explanation:
The equation of the line is y = mx + b
where
m is the slope = rise/run
b = y-intercept ie where the line crosses the y-axis at x = 0
The line crosses the y axis at y = 1 so the y-intercept is 1 and the point at which the line crosses is (0, 1)
We have the equation as
y = mx + 1
To find the slope, take any two points on the line. Find the corresponding difference in the y values and divide this difference by the corresponding difference in the x values
Two convenient points are (0, 1) and (3, 0)
Slope = [tex]\frac{0-1}{3-0} = -\frac{1}{3}[/tex]
Equation of the line :
[tex]y = -\frac{1}{3}x + 1[/tex]
To find out if the inequality in the shaded region is a ≥ or a ≤ inequality, take a point in the shaded region. Determine whether the chosen point x, y values satisfy which of the following equations
[tex]y\le -\frac{1}{3}x + 1[/tex] (1)
or
[tex]y\ge -\frac{1}{3}x + 1[/tex] (2)
The point (0,0) is inside the shaded region
Plug in these values into inequality (1)
[tex]0 = -\frac{1}{3}\cdot0 + 1[/tex] = 1
Is 0 ≤ 1 ?
Indeed it is so the inequality is
[tex]y\le -\frac{1}{3}x + 1[/tex] (Answer)
The region on the opposite side of the line must be a ≥ inqeuality
The attached graph makes it clearer
Find the value of x.
51 m
h
48 m
51 m
Step-by-step explanation:
there is no "x" in the whole scenario.
you and your teacher mean "h" ?
this we get by using Pythagoras, because h, half of the baseline and one of the 51 m sides create a new right-angled triangle :
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.
so, for that new inner triangle we have then
51² = h² + (48/2)² = h² + 24²
2601 = h² + 576
h² = 2025
h = 45 m
whats 5 and 1/5 divided by 3