Answer:
p = -3v: (4, -1)f: (4, -4)d: y = 2Step-by-step explanation:
The equation ...
(x -h)² = 4p(y -k)
is the equation of a parabola with vertex (h, k) and vertex-focus distance of p. When p is negative (as here), it means the focus is below the vertex, and the parabola opens downward. The directrix is p units on the other side of the vertex from the focus.
The vertex for equation ...
(x -4)² = -12(y +1)
is (h, k) = (4, -1). The value of p is (-12/4) = -3, so the focus is (4, -1-3) = (4, -4), and the directrix is y = -1+3 = 2.
_____
Additional comment
As a check on the graph, you can remember that any point on the parabola is equidistant from the focus and directrix. You will notice the vertex is halfway between the focus and directrix, so you know that relationship is true there.
You will also notice that a horizontal line from the focus to the parabola intersects the same distance away from the focus as from the directrix. Thus the parabola distance relation holds at that point as well.
create another show real life multi-step function problems with Solutions in quadratics
Answer:
Kazan also SOS jz zks zj sj aka always zks. aiwow
Instructions: Use the images to answer the questions below.
Graph A
Graph B
Graph C
5108
6 4 8
7046
8 2 2 2 6 66
90 000 24
50,1,2,
63,8,9,
71,3,4,
8 2,4,6,7,
glo,
57 39
68 5 1
7 3 0 0
824
919
an
11.11
1. What type of graph is displayed? stem-and-leaf plot •
2. The data is quantitative
3. Which graph is made correctly? Graph A :
4. The data in the correctly made graph is negatively skewed . This indicated that the mean is
the same or approximately the same as the median.
5. The population size of the data set in the correctly made graph is 5
Some of the sub-questions have been answered. I will provide explanation to the already answered questions and then answer the unanswered parts
1. The graph type
The three graph displayed are stem-and-leaf plots. The single numbers at the left-hand side are referred to as the stem, while the numbers at the right are called leaves.
2. The type of data
The three graphs display numerical data (i.e. numbers). Hence, the data are quantitative
3. The correct graph
To know the correct graph; the leaves on each line must be in ascending order and the delimiter to use is a blank space.
Only graph A obey the above illustration
4. Skewness
In graph A, the length of the leaves increases as we move from one stem to the other. This means that the graph is negatively skewed.
For a negative skewed stem plot, the mean is less than the median
5. The population size
This means that we count the number of leaves in the stem plot
The leaves are:
[tex]Leaves = \{0,8,4,8,0,4,6,2,2,2,6,6,6,0,0,0,0,2,4\}[/tex]
So, the population size is: 19
6. The data set
To do this, we include the stem to the corresponding leaves.
So, we have:
[tex]Dataset= \{50,58,64,68,70,74,76,82,82,82,86,86,86,90,90,90,90,92,94\}[/tex]
Learn more about stem and leaf plots at:
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Can someone explain this
=========================================================
Explanation:
Let x be the unknown angle we want to find. This angle is in degrees.
The diagram shows 19 is the opposite of this angle, and the side 35 is adjacent to the angle.
We use the tangent ratio to tie the two sides together
[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(x) = \frac{19}{35}\\\\x = \tan^{-1}\left(\frac{19}{35}\right)\\\\x \approx 28.4956386\\\\x \approx 28\\\\[/tex]
Note: The notation [tex]\tan^{-1}[/tex] refers to the inverse tangent, or arctangent.
i) [(2⁵)×7³] /(8³×7)
=8³ can be written as =(2×2×2)³
=(2³)³
we have,
=[(2⁵)²×7³) / [(2³)³×7)
=(2⁵×2×7³)/[(2³×3×7) ....(▪︎(Am)n=(amn)
=(2¹⁰×7³)/(2⁹×7)
=(2¹⁰×7³)/(2⁹×7)
=(2¹⁰-a×7³-¹)▪︎▪︎▪︎(▪︎am÷an=am-n)
=2×7²
=2×7×7
=97
-------
It's answer is correct and wrong
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Answer:
its 196
Step-by-step explanation:
Element X is a radioactive isotope such that every 42 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 50 grams, how long
would it be until the mass of the sample reached 45 grams, to the nearest tenth of a
year?
Answer:
6.38548 years
Step-by-step explanation:
1 = 2 [tex]e^{42k}[/tex]
1/2 = [tex]e^{42k}[/tex]
ln(1/2) = 42k ln(e)
ln(1/2)/42 = k
k = -0.01650
~~~~~~~~~~~~~~
45 = 50 [tex]e^{-0.01650t}[/tex]
45/50 = [tex]e^{-0.01650t}[/tex]
ln(45/50) = -0.01650 t ln(e)
ln(45/50)/ -0.01650 = t
t = 6.38548 years
The number of years for the radioactive element to reach a mass of 45 grams is given by t = 6.384129 years
What is half-life of an element?The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
Let the number of years be t
Let the initial mass of the element be a = 50 grams
The final mass of the element be ( a - x ) = 45 grams
Now , Element X is a radioactive isotope such that every 42 years, its mass decreases by half
And , half life t½ = 42 years
So , the decay constant k = 0.693/t½
k = 0.693 / ( 42 )
k = 0.0165
And , k= 2.303/t {log (a/a-x)}
So , t = 2.303 / ( 0.0165 ) log ( 50/45 )
On simplifying , we get
t = 6.384129 years
Hence , the number of years for the radioactive element to reach 45 grams is 6.384129 years
To learn more about half-life of an element click :
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Combine these radicals.
Anyone pls I need
Answer:
-26 sqrt(3)
Step-by-step explanation:
-12 sqrt(12) - 2 sqrt(3)
Rewriting
-12 sqrt(4*3) - 2 sqrt(3)
We know sqrt(ab) = sqrt(a)sqrt(b)
-12 sqrt(4)sqrt(3) - 2 sqrt(3)
-12 (2) sqrt(3) - 2 sqrt(3)
-24 sqrt(3) - 2 sqrt(3)
-26 sqrt(3)
I need help with this
Answer:
45
Step-by-step explanation:
Find the distance between the two points.
(-2,5)
✓ [?]
(4,-2)
Enter the number that
goes beneath the
radical symbol.
Enter
Answer:
√85
Step-by-step explanation:
We can find the distance between two points by using this formula
d = √(x2 - x1)² + (y2 - y1)²
Where the x and y values are derived from the two given points
The two given points are (-2,5) and (4,-2)
Remember that coordinates are written as (x,y)
Next we want to define our variables ( x2, x1, y2 and y1 are the variables)
x2 = 4
x1 = -2
y2 = -2
y1 = 5
Now to find the distance between the two points we simply substitute the values of the variables into the formula
Formula: d = √(x2 - x1)² + (y2 - y1)²
x2 = 4, x1 = -2, y2 = -2 and y1 = 5
d = √(4 - (-2))² + (-2 - 5)²
The two negative signs before the 2 cancel out and it changes to + 2
d = √(4 + 2)² + (-2 - 5)²
Add 4 and 2
d = √6² + (-2 - 5)²
Subtract -2 and -5
d = √6² + -7²
Apply the exponents
d = √36 + 49
Add 36 and 49
d = √85
We can conclude that the distance between the two points is √85
27x + 24y= 4.5
1.5x + y =0.225
Answer:
x = 0.1, y = 0.075
Step-by-step explanation:
Given the 2 equations
27x + 24y = 4.5 → (1)
1.5x + y = 0.225 → (2)
Multiplying (2) by - 24 and adding to (1) will eliminate the y- term
- 36x - 24y = - 5.4 → (3)
Add (1) and (3) term by term to eliminate y
- 9x = - 0.9 ( divide both sides by - 9 )
x = 0.1
Substitute x = 0.1 into either of the 2 equations and solve for y
Substituting into (2)
1.5(0.1) + y = 0.225
0.15 + y = 0.225 ( subtract 0.15 from both sides )
y = 0.075
Answer:
the values for x AND y are 0.1 and 0.075 respectively
(x + 74) − 318 = 200
Answer:
(x + 74) - 318 = 200
x + 74 = 200 + 318
x +74 = 518
x = 518 - 74
x = 444
I hope this is helpful to you.
What percentage is 150 grams of 400 grams?
1 %
Answer:
37.5%
Step-by-step explanation:
150/450 = .375 = 37.5%
The percentage is 150 grams out of 400 grams will be 37.5%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.
The percentage is given as,
Percentage (P) = [Initial value - Final value] / Initial value x 100
It is given that the difference between the initial and final value is 15 grams and the initial value is 400 grams.
Then the percentage is 150 grams out of 400 grams will be
P = (150 / 400) x 100
P = 0.375 x 100
P = 37.5%
Thus, the percentage is 150 grams out of 400 grams will be 37.5%.
More about the percentage link is given below.
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Need help with this, don't understand it. we weren't taught how to do this
9514 1404 393
Answer:
A, C, D, E
Step-by-step explanation:
Any relation that is different from a straight line with a defined constant slope will be a relation that is either or both of ...
not a functionnot linear__
a) degree 3, not linear
b) a linear function
c) a vertical line with undefined slope, not a function
d) a curve opening downward, not linear
e) a line with a bend in the middle, not linear
f) a linear function
What are the coordinates of the vertices of the image?
A) A'(9,8), B'(-3,-4), C'(1, 2), and D'(1,-2)
B) A'(3,4), B'(3,-4), C'(-5, 2), and D'(1, 2)
C) A'(3,8), B'(-3, 4), C'(1,-2), and D'(-1,2)
D) A'(-3, 4), B'(3,4), C'(5,-2), and D'(-1,-2)
Answer:
D
Step-by-step explanation:
I took the quiz
∫(x+1)/(x2+2)2x−3dx need help with this question. can you show the process
do you need to include the wiggle infront of the first bracket? if not;
(x+1) ÷ [(x^2+2) x (2x-3dx)]
x^2 x 2x = 2x^3
x^2 x -3dx = -3dx^3
2 x 2x = 4x
2 x -3dx = - 6dx
i cant find a way to make it equal 0 so i think the answer is just
x+1 over 2x^3 - 3dx^3 + 4x - 6dx as a fraction
5
In the diagram, rhombus ABCD has sides of length 5 cm each and the length of the
diagonal AC is 8 cm.
(a) Find ABC
(b) Calculate the area of rhombus ABCD
Answer:
a) the angle ABC is approximately 106 degrees b) 24
Step-by-step explanation:
1) Using the law of cos
AC*AC= AB*AB+BC*BC-2*AB*BC*cosB
8*8= 5*5+5*5-2*5*5*cosB
64= 50- 50c0sB
cosB= 14/(-50)= -7/25.
B= arccosB= arccos(-7/25)= 106degrees.
2) sinB*sinB= 1- CosB*cosB= 1-49/625= 576/625
sinB= 24/25 (SinB doesn't equal -24/25, because B is between 0 and 180 degrress, so sin B is positive)
3) S= AB*BC*sinB= 5*5*24/25= 24 (area of the rhombus is 24)
How do I find out the square root of a perfect square
THIS IS TIMED I NEED THE ANSWER NOW
Answer:
114 pi or 359
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLY!!
What is the weight (in grams) of a liquid that exactly fills a 182.8 milliliter container if the density of the liquid is 0.135grams over milliliter? Round to the nearest hundredth when necessary, and only enter numerical values, which can include a decimal point
Answer:
24.68 gram
Step-by-step explanation:
Given that :
Volume = 182.8 ml
Density of liquid = 0.135 gram/ml
Recall :
Density = mass (g/ml) / volume (ml)
Substitute the value into the equation :
0.135 = mass / 182.8
Mass = 0.135 * 182.8
Mass = 24.678 gram
Hence, weight = 24.678 grams
Question 1 (1 point)
The perimeter of an iPad Air is 820 mm. Its length is 100 mm less than twice the
width.
If x = the length of the iPad Air and y = the width of the iPad Air, the linear system of
equations that could be used to model this situations is,
2x + 2y = a
bx = cy-d
The value of a is:
Answer:
a is the perimeter which is given as 820 mm.
Step-by-step explanation:
Perimeter, P = 820 mm
Length is 100 m less than twice of width
let the length is x and the width is y.
So,
x = 2 y - 100
P = 2 (x + y)
820 = 2 (2y - 100 + y)
410 = 3 y - 100
3 y = 510
y = 170 mm
x = 2 x 170 - 100 = 240 mm
The equation is
2 x = 2 y = a
where, a is the perimeter which is given as 820 mm.
Apply the distributive property to factor out the greatest common factor.
44+48=
Answer:
(40+4)+(40+48)
=40+(4+8)+4+8(40)
=44+48+12×40
if u add all
=104×40
=4160
Step-by-step explanation:
please help geometry work coordinates
Answer:
(a,a)
Step-by-step explanation:
Keep in mind that the vertical line represents the y axis and the horizontal line represents the x axis
We want to find the coordinates of C
We can do this by looking at the given coordinates and the axis..
We are given that B is at (0,a) and we are given that D is at (a,0)
Now looking at C, we can tell that C shares the same y value as B and the same x value as D
If B has a y value of a and D has an x value of a then C would have an x and y value of a
Hence C would be at (a,a)
(1-sinx+cosx)^2 = 2(1+sinx)(1+cosx)
If you're trying to establish an identity, the given equation is not an identity. The proper identity would be as follows:
(1 - sin(x) + cos(x))² = (1 - sin(x))² + 2 (1 - sin(x)) cos(x) + cos²(x)
… = (1 - 2 sin(x) + sin²(x)) + 2 (1 - sin(x)) cos(x) + cos²(x)
… = 2 - 2 sin(x) + 2 (1 - sin(x)) cos(x)
… = 2 - 2 sin(x) + 2 cos(x) - 2 sin(x) cos(x)
… = 2 (1 - sin(x) + cos(x) - sin(x) cos(x))
… = 2 (1 - sin(x) + cos(x) (1 - sin(x)))
… = 2 (1 - sin(x)) (1 + cos(x))
But if you're trying to solve an equation:
(1 - sin(x) + cos(x))² = 2 (1 + sin(x)) (1 + cos(x))
2 (1 - sin(x)) (1 + cos(x)) = 2 (1 + sin(x)) (1 + cos(x))
(1 - sin(x)) (1 + cos(x)) - (1 + sin(x)) (1 + cos(x)) = 0
(1 + cos(x)) (1 - sin(x) - 1 - sin(x)) = 0
-2 sin(x) (1 + cos(x)) = 0
sin(x) = 0 or 1 + cos(x) = 0
sin(x) = 0 or cos(x) = -1
[x = arcsin(0) + 2nπ or x = arcsin(0) + π + 2nπ] or
… [x = arccos(-1) + 2nπ]
We have arcsin(0) = 0 and arccos(-1) = π, so the solution set reduces to
x = 2nπ or x = (2n + 1)π
(where n is any integer)
factor as the product of two binomials x2+6x-7
Answer:
(x-1)(x+7)
Step-by-step explanation:
did it on a test and got it right :))
Is -46.2 a irrational number
Answer:
No
Step-by-step explanation:
irrational numbers have nonrepeating and non terminating decimals
This decimal stops at one digit so this is a rational number
Answer:
I would say no
Step-by-step explanation:
An irrational number can't be written as a simple fraction.
PLEASE HELP! WILL MARK BRAINLIEST
Answer:
Corresponding angles postulate
Step-by-step explanation:
<3 and <7 are corresponding angles and if corresponding angles are equal, the lines are parallel.
A rectangle has a perimeter of 50m, the ratio between the two side is 32 . Caculator the area of that rectangle?
Answer:
Area of rectangle = 150 cm
Step-by-step explanation:
Given the following data;
Ratio = 3:2 Perimeter = 50mTo find the area of the rectangle;
First of all, we would determine the dimensions (length and width) of the rectangle;
For length;
Length, L = 2x
For width;
Width, W = 3x
Mathematically, the perimeter of a rectangle is given by the formula;
P = 2(L + W)
50 = 2(2x + 3x)
50 = 2(5x)
50 = 10x
x = 50/10
x = 5
Length, L = 2x = 2 * 5 = 10 cm
Width, W = 3x = 3 * 5 = 15 cm
Now, we would find the area of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = length * width
Area of rectangle = 10 * 15
Area of rectangle = 150 cm
find the mean value of the following. 5, 11, 4, 10, 8, 6
find the missing side
Answer:
[tex]\boxed{x=13.89\:km}[/tex]
Step-by-step explanation:
Pythagorean theorem
[tex]x^2=(12^2)+(7^2)[/tex]
[tex]x^2=144+49[/tex]
[tex]x^2=193[/tex]
[tex]x=\sqrt{193}[/tex]
[tex]\boxed{x=13.89\:km}[/tex]
Select all the expressions that represent the difference of the length to width ratios for rectangle A and rectangle B, where W is the width of rectangle A.
Answer:
w+5/w - w+1/2w
w+9/2w
Step-by-step explanation:
Answer:
A&D are corect
Step-by-step explanation:
combine like terms
Which rule is a recursive rule for the sequence
1, – 6, 36, – 216,
...?
Ο o An
-
6. An-1
ο o an
.
6
An-1
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6. An-1
1
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-
.
6
an-1
1
2
3