Answer:
Step-by-step explanation:
Answer:
[tex]y=(x-7)^2-1[/tex]
Step-by-step explanation:
We want to convert the equation:
[tex]\displaystyle y=x^2-14x+48[/tex]
Into vertex form, given by:
[tex]\displaystyle y=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
There are two methods of doing this. We can either: (1) use the vertex formulas or (2) complete the square.
Method 1) Vertex Formulas
Let's use the vertex formulas. First, note that the leading coefficient a of our equation is 1.
Recall that the vertex is given by:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -14, and c = 48. Find the x-coordinate of the vertex:
[tex]\displaystyle x=-\frac{(-14)}{2(1)}=7[/tex]
To find the y-coordinate, substitute this value back into the equation. Hence:
[tex]y=(7)^2-14(7)+48=-1[/tex]
Therefore, our vertex (h, k) is (7, -1), where h = 7 and k = -1.
And since we already determined a = 1, our equation in vertex form is:
[tex]\displaystyle y=(x-7)^2-1[/tex]
Method 2) Completing the Square
We can also complete the square to acquire the vertex form. We have:
[tex]y=x^2-14x+48[/tex]
Factor out the leading coefficient from the first two terms. Since the leading coefficient is one in this case, we do not need to do anything significant:
[tex]y=(x^2-14x)+48[/tex]
Now, we half b and square it. The value of b in this case is -14. Half of -14 is -7 and its square is 49.
We will add this value inside the parentheses. Since we added 49 inside the parentheses, we will also subtract 49 outside to retain the equality of the equation. Hence:
[tex]y=(x^2-14x+49)+48-49[/tex]
Factor using the perfect square trinomial and simplify:
[tex]y=(x-7)^2-1[/tex]
We acquire the same solution as before, with the vertex being (7, -1).
Round 437,912 to the place value of the underlined digit.
O 437,900
437,000
o
438,000
437,000
Yeah
https://youtu.be/ipEbWgC-6nA
1 Construct the following triangles. You will need a ruler and a protractor.
a) Triangle ABC, where AB = 5 cm,
Answer:
abcdefghijklmnopqrstuvwxy and z
Step-by-step explanation:
22. The ratio in which (4, 5) divides the join of (2, 3)
and (7, 8) is :
(a) 4 : 3
(c) 3 : 2
(b) 5:2
(d) 2:3
Let the ratio be m:n
(x,y)=(4,5)Points be (x1,y1)=(2,3)(x2,y2)=(7,8)We know
[tex]\boxed{\sf (x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]
[tex]\\ \sf\longmapsto (4,5)=\left(\dfrac{7m+2n}{m+n},\dfrac{8m+3n}{m+n}\right)[/tex]
Now
.[tex]\\ \sf\longmapsto \dfrac{7m+2n}{m+n}=4\dots(1)[/tex]
[tex]\\ \sf\longmapsto \dfrac{8m+3n}{m+n}=5\dots(2)[/tex]
Adding both
[tex]\\ \sf\longmapsto \dfrac{7m+2n+8m+3n}{m+n}=4+5[/tex]
[tex]\\ \sf\longmapsto \dfrac{7m+8m+2n+3n}{m+n}=9[/tex]
[tex]\\ \sf\longmapsto \dfrac{15m+5n}{m+n}=9[/tex]
[tex]\\ \sf\longmapsto 15m+5n=9(m+n)[/tex]
[tex]\\ \sf\longmapsto 15m+5n=9m+9n[/tex]
[tex]\\ \sf\longmapsto 15m-9m=9n-5n[/tex]
[tex]\\ \sf\longmapsto 6m=4n[/tex]
[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{6}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{3}{2}[/tex]
[tex]\\ \sf\longmapsto m:n=3:2[/tex]
Option B is correct
What is the best point estimate for the population's standard deviation if the sample standard deviation is 37.3
Answer:
The best point estimate for the population's standard deviation is 37.3.
Step-by-step explanation:
Best point estimate:
The best point estimate for the population mean is the sample mean.
The best point estimate for the population standard deviation is the sample standard deviation.
In this question:
Sample standard deviation of 37.3, and thus, the best point estimate for the population's standard deviation is 37.3.
Express 8:28 in its simplest form
Which equation is correct?
1
A. cos x =
sin a
1
B. tan x=
CSC 2
C. sec =
COS
1
D. cot 2 =
sec
SUBMIT
The requried secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x. Option C is correct.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
The correct equation is option C: sec x = 1/cos x.
This is because the secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x.
Learn more about trig ratios here:
https://brainly.com/question/14977354
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Raj wants to get a tropical fish tank. The pet store owner tells him that he needs a tank that has a total volume equal to 80 ounces plus 4 ounces for each fish.
Which model shows two expressions for the total volume of the tank that will hold f fish?
A. 2(2e + 4f + 10g)
B. 80(e + f + g)
C. 2(2e + 2f + 5g)
D. 2(e + 2f + 5g)
Answer:
A. 2(2e + 4f + 10g)
Step-by-step explanation:
Differentiate the x the function :
(3x² - 9x +5²)
Firstly , before solving the equation , we should know about the chain rule and its formula.
Formula For the Chain rule-
$\rightarrow$ $\sf\dfrac\pink{dy}\pink{dx}$=$\sf\dfrac\pink{dy}\pink{du}$ $\times$ $\sf\dfrac\pink{du}\pink{dx}$ $\leftarrow$
_____________________________
$\sf\huge\underline{\underline{Question:}}$
$\sf\small{Differentiate\: x\: the \:function: (3x² - 9x + 5²)}$
$\sf\huge\underline{\underline{Solution:}}$
$\sf{Let\:y = (3x^2 - 9x + 5)^9}$
$\space$
☆ Differentiating both the sides w.r.t.x using chain rule-
$\mapsto$ [tex]\sf\dfrac{dy}{dx}=[/tex][tex]\sf\dfrac{d}{dx}[/tex][tex]\sf{(3x^2 - 9x + 5)^9}[/tex]
$\space$
$\space$
$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] [tex]\times[/tex] [tex]\sf\dfrac{d}{dx}[/tex]$\sf\small{(3x^2-9+5)}$
$\space$
$\space$
$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] [tex]\times[/tex][tex]\sf(6x-9)[/tex]
$\space$
$\space$
$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] $\times$ [tex]\sf{3(2x-3)}[/tex]
$\space$
$\space$
$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{27(3x^2-9x+5)^8(2x-3)}[/tex]
$\space$
$\space$
$\sf\underline\bold\green{❍ dy:dx=27(3x^2-9x+5)^8(2x-3)}$
______________________________
in triangle JKL, angle JKL is a right angle, line KM is an altitude, JL=20, ML=4. Find KM
9514 1404 393
Answer:
KM = 8
Step-by-step explanation:
The ratio of long side to short side is the same for all of the triangles in this geometry:
KM/ML = JM/KM
KM² = ML·JM = 4(20-4) = 64
KM = √64 = 8
The length of KM is 8 units.
what is the simple definition of realnumbers
Answer:
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion).
What is the length of the diagonal of a rectangle with the base of 4 and an altitude of 3
Answer:
5
Step-by-step explanation:
Use the Pythagorean Theorem
C^2=a^2 + b^2
c^2= 3^2 + 4^2
c^2= 9+16
c^2= 25
The take the square root
c= √25
c = 5
In 10 words or fewer, what is the square root of -9?
Type answer here...
What is the square root of -9
Answer:
no solution
Step-by-step explanation:
a negative number cannot be square rooted
Answer:
"not possible". no such thing as a negative squared number
Grasshoppers are distributed at random in a large field according to a Poisson process with parameter a 5 2 per square yard. How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?
In this question, the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Parameter of 5.2 per square yard:
This means that [tex]\mu = 5.2r[/tex], in which r is the radius.
How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?
We want:
[tex]P(X \geq 1) = 1 - P(X = 0) = 0.99[/tex]
Thus:
[tex]P(X = 0) = 1 - 0.99 = 0.01[/tex]
We have that:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5.2r}*(5.2r)^{0}}{(0)!} = e^{-5.2r}[/tex]
Then
[tex]e^{-5.2r} = 0.01[/tex]
[tex]\ln{e^{-5.2r}} = \ln{0.01}[/tex]
[tex]-5.2r = \ln{0.01}[/tex]
[tex]r = -\frac{\ln{0.01}}{5.2}[/tex]
[tex]r = 0.89[/tex]
Thus, the radius should be of at least 0.89.
Another example of a Poisson distribution is found at https://brainly.com/question/24098004
Find the value of x.
X 9 9 7 x = [?]
lee is planning an event for 28 people, he wants to make a fruit drink and he thinks that each person will drink 3 glasses each. If he is correct , how many glasses of fruit should he make?
Answer:
84
Step-by-step explanation:
Since there will be 28 people, and each of them will drink 3 glasses, you just multiply the number of people times the number of glasses they will drink each, so 28*3. The result is 84.
I hope this helped! :D
Lee should need to make 84 glasses of fruit if is planning an event for 28 people.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let Lee needs to make x number of glasses of fruit.
From the question we can frame a linear equation in one variable:
x/3 = 28
As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
After cross multiplication:
x = 28×3
x = 84 glasses
Thus, Lee should need to make 84 glasses of fruit if is planning an event for 28 people.
Learn more about the linear equation here:
brainly.com/question/11897796
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Which graph represents the function h(x) = |x – 3|?
On a coordinate plane, an absolute value graph has a vertex at (0, 3).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
On a coordinate plane, an absolute value graph has a vertex at (3, 0).
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
Answer:
option 3
Step-by-step explanation:
i know because i got it right.
What is the slope of the line that passes through the points (-7, -4) and
(-11, -2)? Write your answer in simplest form.
Answer:
-1/2
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -2 - -4)/( -11 - -7)
=( -2+4)/( -11+7)
= 2 / -4
= -1/2
WILL GIVE BRAINLIEST!!!
f(x) = 2/cos 2x
f(x) = 2/sin1x
f(x)=1/cos1/sin3
{x∣x ≠ π/4+πn/2} , for any integer n
Must click thanks and mark brainliest
Solve the formula for the given variable.
-2x - 6 = 4x
Please helppp
Answer:
s snsnnssjsjjsnsnsjs
es 17 es
Find the lengths of AD, EF, and BC in the trapezoid below.
We know that,
[tex]EF=\dfrac{AD+BC}{2}[/tex]
which is
[tex]x=\dfrac{x-5+2x-4}{2}[/tex]
Now solve for x,
[tex]x=\dfrac{3x-9}{2}[/tex]
[tex]2x=3x-9[/tex]
[tex]x=9[/tex]
Since x is 9, the lengths are,
[tex]AD=x-5=9-5=\boxed{4}[/tex]
[tex]EF=x=\boxed{9}[/tex]
[tex]BC=2x-4=18-4=\boxed{14}[/tex]
Hope this helps :)
Elena drank 3 liters of water yesterday. Jada drank 3/4 times as much water as elena. Link drank twice as much as Jada. Did jada drink more or less then elena? Explain how you know
Answer:
Step-by-step explanation:
3\4 bc on a nuberline it would be 3 3\4
I--I----(etc)
so yeah hope i helped
What number x gives maximum value for c(12,x)?
Answer:
i will say methods try yourself:
How to Determine Maximum Value
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...-x2 + 4x - 2.
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...-x2 + 4x - 2.Since the term with the x2 is negative, you know there will be a maximum point.
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.
.
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plzz follow and make brainlist
Please help on my hw
Answer:
Base is 3 centimeter and hight is 12 cent.
write the equation of the graph, y=? SOMEBODY PLEASE HELP
Answer:
[tex]y=\left(6\right)^{x}\ -3[/tex]
Step-by-step explanation:
What are the coordinates of point K?
A (-2,4)
B (-2,-4)
C (2,-4)
D (2, 4)
Answer:
A
Step-by-step explanation:
I guess that is the answer
Find the distance between the points (-4, -2) and (-8, 6)
Answer:
distance=√[(x2-x1)²+(y2-y1)²]
√[{6-(-2)}²+ (-8-(-4))²]
√(64+16)
√[100]
10
Points given
(-4,-2)(-8,-6)Distance:-
[tex]\\ \sf \longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{(-8+4)^2+(6+2)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{(-4)^2+(8)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{64+16}[/tex]
[tex]\\ \sf \longmapsto \sqrt{80}[/tex]
[tex]\\ \sf \longmapsto 8.4[/tex]
State two similarities and one difference between the graphs of f(x)= 3^x and g (x)= (1/3) ^x
identify an equation in point slope form for the line perpendicular to y=5x=2 that passes through (-6,-1)
Answer:
y=-1/5x-11/5
Step-by-step explanation:
perpendicular, product of both gradients = -1
hence, slope = -1/5
y=-1/5x+c
sub y=-1, x=-6
-1=-1/5(-6)+c
c = -1-6/5=-11/5
y=-1/5x-11/5
Please help as quickly as possible.
Answer:
D
Step-by-step explanation:
take a calculator and try a few points.
I used x = 10.3 and x = 22.
and only D is really getting close to 0.4 and 3.5 as functional results.
Tom and Jerry had a race. Tom started at 0200 running at 4.5km per hour. Jerry started
later at 6:30am running at 6.5km per hour. After five hours, who was ahead, and by how
much (answer in kilometres)
Answer:
Tom, 10.25
Step-by-step explanation:
Distance covered by Tom=4.5*(4 1/2+5)=81/4=42.75km
Distance covered by Jerry=6.5*(5)=32.5km
Tom is ahead from Jerry by 10.25km
