Answer:
[tex]x^{2} -36 = 5x[/tex]
[tex]x^{2} -5x -36 =0[/tex]
(x-9)(x+4) = 0
x = 9 or x= -4
Step-by-step explanation:
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.
Fill in the blank. Given O below, you can conclude that SO is congruent to ___
Answer:
AO
Step-by-step explanation:
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
Two numbers have a sum of 124
Write in algebraic expression
Answer:
Step-by-step explanation:
Let one number = x
Let the other number = y
x + y = 124
You can't go any further than that without more information.
The good news is that no number is excluded.
x = 248
y = -124 for example
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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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:
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)
Recall that variables represent changing values. In this unit, you will work with
equations that contain two different variables. What types of situations might be
modeled with equations containing two or more variables? If the value of one variable
changes, must the value of the other variable change for the equation to remain true?
How would the number of solutions for an equation with two variables differ from the
number of solutions for an equation with only one? Explain
Answer:
It depends on the equations and the variables.
Example of an equation in 2 variables with infinitely many solutions:
sin2x - cos2y + cos2x - sin2y = 0
Example of an equation in 1 variable with 2 solutions:
(x - 1)(x - 2) = 0
Example of 2 equations in 2 variables with no solution:
The intersection of the lines given by
y = 3x + 1
y = 3x + 2
Example of an equation in 1 variable with 1 solution:
5x - 4 = 15
Example of an equation in 1 variable with no real solution:
x2 + 49 = 0
We can go on and on with examples like this. The question is way too general.
Step-by-step explanation:
please mark as brainliest
please mark as brainliest
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.
Helppp and explain please and ty ;)
Answer:
Does this seem right to you?
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°
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:
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
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
What is the monthly net income?? Show work plz
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.
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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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:
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Given the linear equation
[tex]5x+3y-9=0[/tex]
.
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
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
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
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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Find √10 yo the nearest hundredth
Answer:
√10 = 3.16
Step-by-step explanation:
using calculator
√10 = 3.162277660168379
Hundredths is the second decimal place.
Since the next decimal place is less than 5
there is no need to round up
√10 = 3.16
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!
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]
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
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
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
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