Answer:
[tex]\large\boxed{(x-h)^2+(y-v)^2=r^2-\bold{Standard\ form}}\\\boxed{x^2+y^2-2hx-2vy+h^2+v^2-r^2=0-\bold{General\ form}}[/tex]
Step-by-step explanation:
[tex](x-h)^2+(y-v)^2=r^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\x^2-2hx+h^2+y^2-2vy+v^2=r^2\qquad\text{subtract}\ r^2\ \text{from both sides}\\\\x^2+y^2-2hx-2vy+h^2+v^2-r^2=0[/tex]
What is the axis of symmetry of f(x) = -2x2 + 8x - 7
bearing in mind that the squared variable is the "x", and thus this is a vertical parabola, therefore its axis of symmetry will come from the x-coordinate of its vertex.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{+8}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{8}{2(-2)}~,~-7-\cfrac{8^2}{4(-2)} \right)\implies \left( \cfrac{8}{4}~,~-7+8 \right)\implies (2,1) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=2}~\hfill[/tex]
Please help me now please
Answer:
The model represents the expression:
A. 7/8 ÷ 1/8
Step-by-step explanation:
In the question, the number line model represents 7/8 divided into 7 equal units. Each arrow represents a unit and there are a total of seven arrows.
The size of each unit is 1/8 as shown.
Showing that 1/8 divides 7/8 into 7 divisions:
7/8 ÷ 1/8
= 7/8 x 8/1
= 7/1 x 8/8
= 7 x 1
= 7
Hence, the number line represents seven divisions given by 7/8 ÷ 1/8.
20. The perimeter of a square is 72 in. What is its area?
72 in2
18 in2
324 in2
5,184 in2
The formula for perimeter is length + length + width + width
You know that all the sides of a square are equal to each other. That means that all the values in the perimeter formula should be the same. Therefore you can divide 72 by 4 (perimeter divided by the number of sides)
72 / 4 = 18
^^^Each side is 18 in
The formula for are is...
A = length x width
so...
18 * 18 = 324
324 in^2
Hope this helped!
~Just a girl in love with Shawn Mendes
If 100 mL of a solution contains 20 g, how many milligrams will 20 mL contain?
Answer:
There are 4,000 milligrams
Step-by-step explanation:
We know that in 1 gram there are 1000 milligrams
To calculate how many milligrams equals 20 grams we perform the following operation
[tex]20\ g*\frac{1000\ mg}{1\ g}=20,000\ mg[/tex]
Then 100 mL of a solution contains 20,000 mg
To calculate how many milligrams there are in 20mL of the solution we perform the following operation
[tex]20\ mL*\frac{20,000\ mg}{100\ mL}=4,000\ mg[/tex]
Can someone please help me out with this question?
Answer:
[tex]\frac{300}{t}[/tex] chairs at each table
Step-by-step explanation:
Total number of chairs : 300
Total number of tables : t
If we divide 300 chairs equally among t tables, then each table must have 300 chairs ÷ t tables = [tex]\frac{300}{t}[/tex] chairs at each table.
If (-3, y) lies on the graph of y = 3^x, then y =
Answer:
y = [tex]\frac{1}{27}[/tex]
Step-by-step explanation:
Given
y = [tex]3^{x}[/tex] and (- 3, y) is a point on the graph, then
y = [tex]3^{-3}[/tex] = [tex]\frac{1}{3^{3} }[/tex] = [tex]\frac{1}{27}[/tex]
Answer: The required value of y is [tex]\dfrac{1}{27}.[/tex]
Step-by-step explanation: We are given that the point (-3, y) lies on the graph of the following equation :
[tex]y=3^x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the value of y.
Since the point (-3, y) lies on the graph of equation (i), so it will satisfy the equation.
Therefore, substituting (-3, y) in equation (i), we get
[tex]y=3^{-3}\\\\\Rightarrow y=\dfrac{1}{3^3}\\\\\\\Rightarrow y=\dfrac{1}{27}.[/tex]
Thus, the required value of y is [tex]\dfrac{1}{27}.[/tex]
which sentence explains why the slope of AB is equal to the slope of BC?
Answer:
Since AB = BE and DB =CE
Step-by-step explanation:
The ratio and of these two give the concept of slope
The last sentence explains why the slope of AB is equal to slope of BC.
What is a slope?It is the measure of steepness of a line.
In the given figure, AD = BE and DB = EC
So, the ratio AD to BE is equal to the ratio BE to EC.
The slope of a line is given by,
slope = rise / run
Which is same as the above mentioned ratio.
Since AD = BE and DB = EC, their proportions are also equal. Therefore the slope of AB is equal to the slope of BC.
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determine the slope of each pair with fractions
Answer:
Step-by-step explanation:
The slope here is -3.
This answer is found by using the formula I clipped below.
Hope that Helps!
What is the equation of the following line? (-3,1) and (0,0)
Answer:
y = (1/3)x
Step-by-step explanation:
If the y-intercept is (0, 0), then y = mx + b becomes y = mx.
Seeing that y increases by 1, going from (-3, 1) to (0, 0), and that x increases by 3, we determine that the slope, m, is 1/3.
The equation of this line is therefore y = (1/3)x.
Answer:it’s Y = - 1/3
Step-by-step explanation:
Need help plz and thank you
Answer:
y = 3x + 1
Step-by-step explanation:
The equation is in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (1, 4) ← 2 ordered pairs from table
m = [tex]\frac{4-1}{1-0}[/tex] = 3
Note the line crosses the y- axis at (0, 1) ⇒ c = 1
y = 3x + 1
Use the graph to complete the statements.
Answer:
the slope of jk is -6/5
the slope of pq is 4/5
the lines are (I don't know what options are given)
Step-by-step explanation:
you can use the x1 y1 formula
[tex]\frac{y2-y1}{x2-x1}[/tex]=[tex]\frac{-7-5}{10-0}[/tex]=[tex]\frac{-12}{10}[/tex]=[tex]\frac{-6}{5}[/tex]
therefore, the slope is -6/5
using the same formula;
tex]\frac{y2-y1}{x2-x1}[/tex]= [tex]\frac{4-(-8)}{0-(-5)}[/tex]=[tex]\frac{12}{15}[/tex]=[tex]\frac{4}{5}[/tex]
therefore, the slope is 4/5
and I would glady re-edit this answer if you can comment what the options for the last one are :)
Answer:
The slope of Jk is -6/5
The slope of PQ is 4/5
The lines are neither parallel or perpendicular
Step-by-step explanation:
Consider the function g(x)=10/x
Answer:
The correct answers are:
(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0
Step-by-step explanation:
(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.
Rational Function = g(x) =
Denominator = x = 0
Hence the vertical asymptote is x = 0.
(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:
Given function = g(x) =
We can write it as:
g(x) =
If power of x in numerator is less than the power of x in denominator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denominator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denominator).
If power of x in numerator is greater than the power of x in denominator, then there will be no horizontal asymptote.
In above case, 0 < 1, therefore, the horizontal asymptote is y =
The data set represents the total number of tuba players in each of 11 different school band
0,1,3,3, 4, 4, 4, 5, 6, 6, 8
What is the lower quartile of the data?
O
1
ooo
Answer:
3
Step-by-step explanation:
To find the lower quartile first locate the median.
The median is the middle value of the data set arranged in ascending order.
The data given is in ascending order
0, 1, 3, 3, 4, 4, 4, 5, 6, 6, 8
↑ ← The median is 4
The lower quartile is then the middle value of the data to the left of the median.
0, 1, 3, 3, 4
↑ ← the lower quartile is 3
The lower quartile of the data is given as 3
What is lower quartile of the data?Lower quartile of the data is the median of all the observations till the median of the given observations.
What is median?Median is the middle observations of the set of observations.
How to find the what is the lower quartile of the data?First we should find the median of given observations.The median is the mid value which is 4
So, the values till 4 are 0, 1 , 3, 3, 4,
Now we have to find the median of these observations.∴ The median is the mid value which are 3
∴ The lower quartile of the data is given as 3
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Find the indicated side of the triangle.
Please Help!!!
Answer:
Step-by-step explanation:
So you can use the special formula for 30-60-90 triangle or you can use the whole Soh Cah Toa thing.
I honestly prefer trig. so a is the opposite side of the 30 deg and 12 is the hyp. This should scream sine to you since sine goes with opposite/hypotenuse.
sin(30 deg)=a/12
Multiply both sides by 12
giving a=12 sin(30)
Type into calculator unless you know your unit circle well.
a=6
Answer:
a = 6
Step-by-step explanation:
Since the triangle is right use the sine ratio to find a
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{12}[/tex]
Multiply both sides by 12
12 × sin30° = a, hence
a = 6
Choose the correct simplification of (3x3y4z4)(2x3y4z2)
Answer:
6x^6y^8z^6
Step-by-step explanation:
(3x^3y^4z^4)(2x^3y^4z^2)
= 6x^(3+3) y^(4+4) z^(4+2)
= 6x^6y^8z^6
Answer:
(6x⁶y⁸z⁶)
Step-by-step explanation:
The given expression is (3x³y⁴z⁴) (2x³y⁴z²) and we have to simplify it.
= 6 (x)³⁺³ (y)⁴⁺⁴ (z)⁴⁺² [Since xᵃ · xᵇ = xᵃ⁺ᵇ]
Therefore, simplified form of the expression is
(6x⁶y⁸z⁶)
what values complete this function
Answer:
f(x) = - (x - 3) (x + 4)
Step-by-step explanation:
* Lets explain the graph
- The graph is a parabola, which is the graph of the quadratic function
- The general form of the quadratic function is f(x) = ax² + bx + c
- a is the coefficient of x², if a > 0 the parabola is oped upward, if a < 0
the parabola is opened down ward
- c is the y-intercept of the parabola means the curve intersect the
y-axis at point (0 , c)
- The roots (zeroes) of the quadratic function are the x-intercept of the
parabola means values of x when f(x) = 0
* Now lets solve the problem
- The parabola is downward
∴ The coefficient of x² is negative
- The y-intercept is 12
∴ c = 12
- The x-intercepts are 3 , -4
∴ The zeroes of the function are 3 , -4
∴ x = 3 ⇒ subtract 3 from both sides
∴ x - 3 = 0
∴ x = -4 ⇒ add 4 for both sides
∴ x + 4 = 0
- The factors of f(x) are (x - 3) and (x + 4)
∴ f(x) = -(x - 3)(x + 4)
- Lets find the general form of the function to be sure from the answer
- Multiply the two brackets
∵ f(x) = - [(x)(x) + (x)(4) + (-3)(x) + (-3)(4)] = - [x² + 4x + -3x + -12]
∴ f(x) = - [x² + x - 12] ⇒ multiply the bract by the (-)
∴ f(x) = -x² - x + 12
- Lets check the value of the y-intercept
∵ a = -1 , c = 12
∴ The coefficient of x² is -ve ⇒ the parabola is downward
∴ The y-intercept is 12
∴ f(x) = - (x - 3) (x + 4) is the answer
Solve system of equations 2x + 2y + 5z = 7 6x + 8y + 5z = 9 2x + 3y + 5z = 6
Answer:
the values of x, y and z are x= 2, y =-1 and z=1
Step-by-step explanation:
We need to solve the following system of equations.
We will use elimination method to solve these equations and find the values of x, y and z.
2x + 2y + 5z = 7 eq(1)
6x + 8y + 5z = 9 eq(2)
2x + 3y + 5z = 6 eq(3)
Subtracting eq(1) and eq(3)
2x + 2y + 5z = 7
2x + 3y + 5z = 6
- - - -
_____________
0 -y + 0 = 1
-y = 1
=> y = -1
Subtracting eq(2) and eq(3)
6x + 8y + 5z = 9
2x + 3y + 5z = 6
- - - -
______________
4x + 5y +0z = 3
4x + 5y = 3 eq(4)
Putting value of y = -1 in equation 4
4x + 5y = 3
4x + 5(-1) = 3
4x -5 = 3
4x = 3+5
4x = 8
x= 8/4
x = 2
Putting value of x=2 and y=-1 in eq(1)
2x + 2y + 5z = 7
2(2) + 2(-1) + 5z = 7
4 -2 + 5z = 7
2 + 5z = 7
5z = 7 -2
5z = 5
z = 5/5
z = 1
So, the values of x, y and z are x= 2, y =-1 and z=1
Durind the summer, Ms. Stevenson likes to swim. Her goal next summer is to swim1,456 laps. If she swims 28 laps a day, how many days will it take Ms. Stevenson to reach her goal?
Answer:
52
Step-by-step explanation:
1456/ 28 = 52 days
Answer:
52 days
Step-by-step explanation:
If she swims 28 laps a day, it will take her 52 days to reach her goal.
1,456/28 = 52
Which line represents the line that passes through (3/2-1/2) and has a slope of 1
Step-by-step explanation:
The point-slope of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have
[tex]m=1\\\\\left(\dfrac{3}{2},\ -\dfrac{1}{2}\right)\to x_1=\dfrac{3}{2},\ y_1=-\dfrac{1}{2}[/tex]
Substitute:
[tex]y-\left(-\dfrac{1}{2}\right)=1\left(x-\dfrac{3}{2}\right)[/tex]
[tex]y+\dfrac{1}{2}=1\left(x-\dfrac{3}{2}\right)[/tex] → the point-slope form
Convert to the slope-intercept form:
[tex]y+\dfrac{1}{2}=x-\dfrac{3}{2}[/tex] subtract 1/2 from both sides
[tex]y=x-\dfrac{4}{2}[/tex]
[tex]y=x-2[/tex] → the slope-intercept form
If a plane can climb at 2,400 feet per minute, how many minutes are needed to climb to 60,000 feet?
Make a Selection:
A. 18
B. 25
C.15
D.12
Answer:
b
Step-by-step explanation:
25 minutes
Answer:
B.25
Step-by-step explanation:
To find the amount of minutes, divide the total amount of feet from the feet per minute:
60000/2400 = 25
B. 25 is the amount needed to climb to 60,000 feet.
~
Line n has no x-intercept and it’s y-intercept is (0,-4)
Answer:
y = -4Step-by-step explanation:
If the line has no x-intercept, then it's a horizontal line with equation
[tex]y=a,\ a\neq0[/tex]
The line passes through the point (0, -4). Therefore the equation of this line is:
[tex]y=-4[/tex]
Answer:
y = 4
Step-by-step explanation:
Since the line has no x-intercept, this means that the line has a slope of 0, meaning it is a horizontal line. So with the equation y = mx + b, mx cancels out to 0 because there is no slope. This leaves y = b, where b = 4. So the answer is y =4
Lines L and K are parallel; what is the value of a + b?
Answer:
135°
Step-by-step explanation:
Draw a line that intersects the endpoint of the angle that is between L and K and is also perpendicular to L and K.
∠a+45°+∠b = 180°
∠a+∠b = 135°
What is the slope of the line shown in the graph? A coordinate plane graph is shown. Points are plotted at 0 comma 3 and 1 comma 1. The points are joined by a line. −1 −2 negative 1 over 2 2
The slope of the line shown in the graph is -2.
The slope of a line can be found using the formula slope = (change in y) / (change in x).
Given the points (0, 3) and (1, 1),
we can calculate the slope by finding the difference in y-coordinates and dividing it by the difference in x-coordinates.
Slope = (1 - 3) / (1 - 0) = -2.
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The diagram shows a sector of a circle with radius 15 cm.
Calculate the perimeter of this sector.
Answer:
≈ 36.81 cm ( to 2 dec. places )
Step-by-step explanation:
The perimeter (P) of the sector is calculated as
P = circumference of circle × fraction of circle + radii
= 2π × 15 × [tex]\frac{26}{360}[/tex] + 30
= 30π × [tex]\frac{26}{360}[/tex] + 30
= [tex]\frac{26\pi }{12}[/tex] + 30 ≈ 36.81 cm
Answer:
36.81 cm to the nearest hundredth (or 30 + 13 π / 6).
Step-by-step explanation:
The perimeter of the circle of which this sector is a part = 2 π 15
= 30 π cms
So the length of the curved part of the sector = 26 * 30 π / 360
= 2.167π
The perimeter = 2(15) + 2.167 π
= 36.81 cm.
if Angle AOC =85 and angle BOC=2x+10 and angleAOB=4x-15 find the degress measure of BOC and AOB
Answer:
m angle BOC 120
m angle AOB 205
Step-by-step explanation:
So you are given mangle AOC+mangle BOC=mangle AOB.
mangle means measure of angle.
Let's do some substituting into our equation.
85+2x+10=4x-15
Solve for x... First I'm going to combine the like terms on the left hand side:
95+2x=4x-15
Add 15 on both sides
110+2x=4x
Subtract 2x on both sides
110 =2x
Divide both sides by 2
110/2 =x
x =110/2
x =55
So Recall mangle BOC=2x+10 =2(55)+10=110+10=120
And you also have mangle AOB=4x-15=4(55)-15=220-15=205
The question is in the image. ( please answer ASAP)
Answer:
A.
male long sleeves: 3
Male short sleeves: 0
male rolled up sleeves: 2
Female long sleeves: 0
Female short sleeves: 2
Female rolled up sleeves: 1
B. 0/3
C. 2/5
Step-by-step explanation:
HELLPP
What is economic utility
Hello There!
Economic utility is the amount of satisfaction a consumer receives from the consumption of a particular product or service.
Answer:
The capacity of a good or service to meet the demand of a consumer. The amount of economic utility of a good or service determines what the demand will be for that good or service, which impacts the price that people will be willing to pay to obtain it
Step-by-step explanation:------------------------------------------)-
One x-intercept of a parabola is at the point (-3,0). Use the factor method to find the other x-intercept for the parabola defined by this equation:
y= -x^2-5x-6
Separate values with a comma
Answer:
The other x-intercept is (-2,0)
Step-by-step explanation:
-x^2-5x-6
-(x^2+5x+6)
We know x=-3 is a x-intercept so x+3 is a factor
-(x+3)( )
The other factor has to be x+2 since 3(2)=6 and 2+3=5
So -x^2-5x-6 is the same as -(x+3)(x+2)
Which means the other x-intercept is (-2,0)
A car travels a distance of 104 miles in 4 hours. What is the speed in miles per hour?
Please do now
Answer:
26 mph
Step-by-step explanation:
d/t = r (distance/ time = rate)
104/4 = 26
We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.
Each card will have:
i) One rank from 1 to 15.
ii) One of 9 different suits.
Hence, there are 135 cards in the deck with 15 ranks for each of the 9 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!
The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.
a) How many different ways are there to get any 5 card hand?
The number of ways of getting any 5 card hand is
Answer:
Step-by-step explanation:
There are 5 cards we are selecting out of 135 cards so how many ways can we draw 5 cards at a time (w/o replacement)
There are 135 ways to choose the first card.
There are then 134 ways to choose the second card.
There are then 133 ways to choose the third card.
132 to choose the 4th
131 to choose the 5th.
Now multiply those giving 135*134*133*132*131 or you could have just said
135 P 5.
In case you don't know P means permutation.
The mathematics behind determining the number of different ways to get any 5 card hand from a deck of 135 cards involves combinatorics. Specifically, the combinations formula is used, which is C(n, r) = n! / [(n-r)!r!]. In this case, n is 135 (the total number of cards) and r is 5 (the number of cards drawn).
Explanation:The subject of this question concerns probabilities in the game theory section of mathematics, specifically revolving around understanding the combinatorics of card hands in a uniquely structured card game.
Using combinatorial mathematics, the number of ways to get any 5-card hand from a deck of 135 cards can be calculated by using the combinations formula which is: C(n, r) = n! / [(n-r)!r!]. In this instance, 'n' represents the number of total outcomes (135 cards) and 'r' is the number of outcomes chosen at a time (5 cards).
So to find the number of 5-card hands, you would calculate it as follows:
C(135, 5) = 135! / [(135-5)!5!]
The factorial of a number, denoted as '!', is the product of the number and all the consecutive numbers below it down to 1. So 5! = 5*4*3*2*1. Calculating this large of a number directly can be a bit tricky, but there are online tools that can help!
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