Answer:
3
Step-by-step explanation:
slope = (y2-y1)/(x2-x1)
(-4-2)/(-4--2)
-6/-2
3
Answer:
to find slope we use the following methods
Step-by-step explanation:
given
X1 -2
X2= -4
Y1= 2
Y2= -4
slope=y2-Y1 ÷X2-X1
= -4-2÷ -4-(-2)
=-6 ÷-4+2
= -6÷-2
= 3
slop of (-2,2) (-4,-4) = 3
what is the equation of the parabola with focus (-1/4,-2/3) and directrix y=3/4?
A. y = -x^2 +8x -7
B. y = -1/2x^2 +14/5x +17/53
C. y = -6/17x^2 - 3/17x +1/51
D. y = -1/6x^2
Given:
Focus of the parabola = [tex]\left(-\dfrac{1}{4},-\dfrac{2}{3}\right)[/tex]
Directrix of the parabola is [tex]y=\dfrac{3}{4}[/tex].
To find:
The equation of the parabola.
Solution:
The equation of the parabola is:
[tex](x-h)^2=4p(y-k)[/tex] ...(i)
Where, (h,k) is vertex, (h,k+p) is focus and [tex]y=k-p[/tex] is the directrix.
It is given that the focus of the parabola is at [tex][/tex].
[tex](h,k+p)=\left(-\dfrac{1}{4},-\dfrac{2}{3}\right)[/tex]
On comparing both sides, we get
[tex]h=-\dfrac{1}{4}[/tex]
[tex]k+p=-\dfrac{2}{3}[/tex] ...(ii)
Directrix of the parabola is [tex]y=\dfrac{3}{4}[/tex]. So,
[tex]k-p=\dfrac{3}{4}[/tex] ...(iii)
Adding (ii) and (iii), we get
[tex]2k=-\dfrac{2}{3}+\dfrac{3}{4}[/tex]
[tex]2k=\dfrac{-8+9}{12}[/tex]
[tex]k=\dfrac{1}{12\times 2}[/tex]
[tex]k=\dfrac{1}{24}[/tex]
Putting [tex]k=\dfrac{1}{24}[/tex] in (ii), we get
[tex]\dfrac{1}{24}+p=-\dfrac{2}{3}[/tex]
[tex]p=-\dfrac{2}{3}-\dfrac{1}{24}[/tex]
[tex]p=\dfrac{-16-1}{24}[/tex]
[tex]p=\dfrac{-17}{24}[/tex]
Putting [tex]h=-\dfrac{1}{4},k=\dfrac{1}{24}, p=-\dfrac{17}{24}[/tex] in (i), we get
[tex]\left(x-(-\dfrac{1}{4})\right)^2=4\left(-\dfrac{17}{24}\right)\left(y-\dfrac{1}{24}\right)[/tex]
[tex]\left(x+\dfrac{1}{4}\right)^2=-\dfrac{17}{6}\left(y-\dfrac{1}{24}\right)[/tex]
[tex]x^2+2(x)(\dfrac{1}{4})+(\dfrac{1}{4})^2=-\dfrac{17}{6}\left(y-\dfrac{1}{24}\right)[/tex]
[tex]-\dfrac{6}{17}\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)=y-\dfrac{1}{24}[/tex]
On further simplification, we get
[tex]-\dfrac{6}{17}(x^2)-\dfrac{6}{17}(\dfrac{1}{2}x)-\dfrac{6}{17}(\dfrac{1}{16})=y-\dfrac{1}{24}[/tex]
[tex]-\dfrac{6}{17}x^2-\dfrac{3}{17}x-\dfrac{3}{136}+\dfrac{1}{24}=y[/tex]
[tex]-\dfrac{6}{17}x^2-\dfrac{3}{17}x+\dfrac{-9+17}{408}=y[/tex]
[tex]-\dfrac{6}{17}x^2-\dfrac{3}{17}x+\dfrac{8}{408}=y[/tex]
[tex]-\dfrac{6}{17}x^2-\dfrac{3}{17}x+\dfrac{1}{51}=y[/tex]
Therefore, the equation of the parabola is [tex]y=-\dfrac{6}{17}x^2-\dfrac{3}{17}x+\dfrac{1}{51}[/tex]. Hence, the correct option is C.
A textbook store sold a combined total of 361 chemistry and biology textbooks in a week the number of chemistry textbooks sold was 45 more than the number of biology textbooks sold.how many textbooks of each type were sold?
Answer:
Chemistry Books- 203 and Biology Books- 158
Step-by-step explanation:
I'm not sure myself how I did it since I don't have an exact method but I can guarantee that the answer is correct. (Quick sum-up of what I kinda did though. Divide both numbers by 2, then added (22, about half of 45), add 180 (about half of 361) and then subtracted 202 from 361. Realized that it was one off so I just made it 203 and 158)
Sorry for the mess of an explanation but hope it helps!
At 7am the temperature was -4 degrees. by 3pm the temperature had gone up by 10 degrees. what was the temperature at 3am
Answer:
6 degrees
Step-by-step explanation:
[tex] - 4 + 10 = 6[/tex]
Answer:
6 degrees
Step-by-step explanation:
if f(x)=x-3/x and g(x) = 5x – 4, what is the domain of (fog)(x)?
Answer:
x = 4/5 is the one x value that is not permitted. The domain of (fog)(x) is
(-infinity, 4/5) ∪ (4/5, infinity)
Step-by-step explanation:
(fog)(x) is the "composition" of f and g. We start with f(x) and replace x with g(x), which is 5x - 4:
3
f(x) = x - ------- becomes
x
3
f(5x - 4) = [5x - 4] - ------------
[5x - 4]
To identify the domain, consider the value or values of x for which the denominator shown above is zero: 5x - 4 = 0, or 5x = 4, or x = 4/5
The domain of the composite function (f·g)(x) in interval notation is (-∞,0)∪(0,∞).
What is domain and range of the function?The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.
The given functions are f(x)= x-3/x and g(X)=5x-4.
Now, (f·g)(x)=f(x)×g(x)
= (x-3/x)(5x-4)
(f·g)(x)= 5x²-15-4x+12/x
Find the domain by finding where the expression is defined.
Interval Notation: (-∞,0)∪(0,∞)
Set-Builder Notation:{x|x≠0}
Therefore, the domain of the composite function (f·g)(x) in interval notation is (-∞,0)∪(0,∞).
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On the last day of a Shakespeare class, an English teacher asked her students which play
they liked the best, and she recorded the results to date.
2 liked Hamlet
8 liked Twelfth Night
2 liked a Midsummer Night's Dream
What is the experimental probability that the next student to respond likes Hamlet best?
Write your answer as a fraction or whole number
Answer:
ok so if we add this up we get that there is 14 kids in the class who have been polled and 2/14 or 1/7 likes hamlet so the chance is 1 out of 7
The experimental probability that the next student to respond likes Hamlet best is [tex]\frac{1}{6}[/tex] .
Concept:Probability = [tex]\frac{Favourable \ Outcomes }{Total \ Outcomes}[/tex]To find total outcomes, we will add all the students.To find the favorable outcomes, we will count the number of students that likes hamlet.How to solve the given question?Probability = [tex]\frac{Favourable \ Outcomes }{Total \ Outcomes}[/tex]Total Outcomes = 2 + 8 + 2 = 12Favorable outcomes = 2∴ [tex]P(E) = \frac{Favourable \ Outcomes }{Total \ Outcomes} = \frac{2}{12} =\frac{1}{6}[/tex]Thus, the experimental probability that the next student to respond likes Hamlet best is [tex]\frac{1}{6}[/tex] .
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Which of the following statements is true for this distribution? (No calculations are required to answer this question.)
50
60
70
80
O A Mean > Median
O
B. The relationship between the mean and median cannot be determined from the display.
O
C. Median > Mean
O D. Mean = Median
Answer:
The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.
Hence, the correct option is A.
To estimate the population mean we use a t-distribution to calculate the confidence interval. When we use a t-distribution the sample standard deviation is used to estimate the population standard deviation
What is the monthly net income?? Show work plz
Helppp and explain please and ty ;)
Answer:
Does this seem right to you?
10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.
Answer:
0.2992 = 29.92% probability of obtaining at least 8 failures.
Step-by-step explanation:
For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A success is 5 or 6.
A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:
[tex]p = \frac{4}{6} = 0.6667[/tex]
10 normal six sided dice are thrown.
This means that [tex]n = 10[/tex]
Find the probability of obtaining at least 8 failures.
This is:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951[/tex]
[tex]P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867[/tex]
[tex]P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174[/tex]
Then
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992[/tex]
0.2992 = 29.92% probability of obtaining at least 8 failures.
if f(x)=3x-1 and g(x)=x+2, find (f-g)(x)
Answer:
2x - 3
Step-by-step explanation:
3x-1 - (x+2)
3x-1 -x -2
2x - 3
Find The Measure Of D
Answer:
138 Degrees
Step-by-step explanation:
Because it is adjacent to the 42 degrees, just subtract 42 from 180 to get 138 degrees.
Answer:
D+42*=180*
D=180-42
138
Step-by-step explanation:
mark as brainiest please
which statment descirbes the soloution to a equation
a+5(2a-1)+3=11a-2
Answer:
Any real number.
Step-by-step explanation:
I dunno what you're asking, but Im assuming you need what a equals to.
[tex]a+5(2a-1)+3=11a-2\\a+10a-5+3=11a-2\\11a-2=11a-2\\[/tex]
The answer is any real number.
the measures of the angles of a triangle are shown in the figure. solve for x
Answer:
solution,
x+41+59=180⁰ ( the sum of total angle of triangle is 180⁰)
or, x+ 100=180
or, X=180-100
so , X=80
Step-by-step explanation:
let us check
59+41+80=180
13-?=7-2x
In the equation above what must ? be so that x has value of 2
Answer:
? = 10
Step-by-step explanation:
13 - (10) = 7-4 ....... 2×2 =4
3 = 3
How many solutions exist for the system of equations in the graph?
Answer:
Two solutions
Step-by-step explanation:
The number of points of intersections represents the number of solutions to the system of equations. Since the parabola intersects the circle at two points, there are two solutions to the circle.
Furthermore, these two points of intersection are exactly the solutions to the system of equations. Finding the coordinates of the points of intersection will give you the solutions to the system of equations.
Who hates math? I'm not too fond of math, but I love numbers.
I am math lover .Before I am also not too fond of math , but if you practiced it will be easy and you loves to do maths and your interest will increase .Sorry for late Answer of attachment will be 5190.
hope it is helpful to you
Answer:
your answer will be 5,190
Step-by-step explanation:
fist you have to subtract 80 from 599 and u will get 519 then you multiply to get the answer
I am also not so good in Math so I still try to help u
Help me solve this problem please
Answer:
actually what is this is you is this a geometry, trigonometry I don't know what to call
line m is perpendicular to line n if the slope of line m is 3/2 what is the slope of line n
Answer:
definantly 3/2
Step-by-step explanation:
perpendicular means same slope
10. What are the coordinates of point on the directed segment from A(2,-3) to B(8,-6) that
partitions the segment such that AC:CB is 4:2?
(1) (6,-5)
(3) (2,0)
(2) (-2, 2)
(4) (1, 1)
Answer:
(4, -4)
Step-by-step explanation:
Using the midpoint formula;
M(X,Y) = {(ax1+bx2)/a+b, (ay1+by2)/a+b}
X = (ax1+bx2)/a+b
Y = (ay1+by2)/a+b
Substitute
X = 4(2)+2(8)/4+2
X = 8+16/6
X = 24/6
X = 4
Also
Y = 4(-3)+2(-6)/6
Y = -12-12/6
Y = -24/6
Y = -4
Hence the required partition is (4, -4)
the slope of line (-1,1) (2,-5)?
Answer:
slope = 4/3
Step-by-step explanation:
(-1 , 1) = (x1 , y1)
(2 , 5) = (x2 , y2)
slope (m) = y2 - y1/x2 - x1
=5 - 1/2 - (-1)
=4 /2+1
=4/3
answer choices:
a. 111
b. 69
c. 86
d. 71
Answer:
b
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ 1 is an exterior angle of the triangle , then
∠ 1 = 30° + 39° = 69°
Answer:
option b: 69°
Step-by-step explanation:
the sum of the interior angles of a triangle is 180c.
that is, 39 + 30 + x = 180
x = 180 - 39 - 30
x = 111°
∠ 1 + x = 180° [ straight line angles ]
∠1 + 111° = 180°
∠1 = 180 - 111 = 69°
Drag the items to complete the sentences about the end behavior of the exponential function graphed.
Answer:
as x --> oo, f(x) = oo (infinite)
as x -- -oo, f(x) = 3
A car left the house traveling north at 10 A.M. Another car left the house traveling south two hours later. If the cars traveled at the same rate and were 550 miles apart at 4 P.M , what was the rate of each car.
Answer:
55 mph
Step-by-step explanation:
What is the slope of the line on the graph below?
5
4
3
4
1
54 321
1 2 3 4 5 X
wy
-
0
Answer:
positive slope
Step-by-step explanation:
when a graph is sloping to the right it means it has a positive . the gradient of this straight is positive .
gradient of the line is greater than 0
The slope of the line is m = 2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 1 , 3 )
Let the second point be Q ( 0 , 1 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 3 - 1 ) / ( 1 - 0 )
m = 2
Therefore , the value of m is 2
Hence , the slope is 2
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The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?
s = StartFraction 3 Over 10 EndFraction m
s = StartFraction 10 Over 3 EndFraction m
m = StartFraction 3 Over 10 EndFraction s
m = StartFraction 1 Over 30 EndFraction s
Answer:
it is b
Step-by-step explanation:
Answer:
it is b
Step-by-step explanation:
A girl runs 2 km in 1 hour . How long will she take to ran 500 m ?
Answer:
1/4 he
Step-by-step explanation:
Answer:
1/4 hour
Step-by-step explanation:
convert 2 km to m
1 km = 1000m
2 km = 2*1000 m
=2000 m
distance time taken
2000 m 1 hour
500 m let be x
2000/500 = 1/x
do cross multiplication
500*1 = 2000*x
500/2000 = x
1/4 = x
Help
Will
Give
Brainlist
Math
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
╭⋟───────────────
Sentence ⇻ The product of - 11 & - 7 gives 77.
Equation ⇻ [tex]\boxed{-11(-7)=77}[/tex].
───────────────⋞╯
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex] RainbowSalt2^{2}2^{2}[/tex] ❦
Answer:
-11(-7) = 77
Step-by-step explanation:
"and" = multiplication sign in maths
pls tell the answer in step by step
Answer:
5
Step-by-step explanation:
here, the highest degree is 5 so the degree of polynomial is also 5.
a rectangle is twice as long as it is wide and its perimeter is 432cm
a) work out the dimensions of the rectangle.
b) work out the area of the rectangle.
Let
Width of rectangle=xLength of rectangle=2xPerimeter=432cmWe know that in a rectangle
☆ Perimeter=2(Length+Breadth)
[tex]\\ \sf\longmapsto 2(x+2x)=432[/tex]
[tex]\\ \sf\longmapsto 2x+4x=432[/tex]
[tex]\\ \sf\longmapsto 6x=432[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{432}{6}[/tex]
[tex]\\ \sf\longmapsto x=72[/tex]
[tex]\\ \sf\longmapsto 2x=2(72)=144[/tex]
Length=144cmBreadth=72cm☆Area=Length×Breadth
[tex]\\ \sf\longmapsto Area=144\times 72[/tex]
[tex]\\ \sf\longmapsto Area=10368cm^2[/tex]
Given the linear equation
[tex]5x+3y-9=0[/tex]
.