Find the coordinates of the focus and equation of the directrix for the parabola given by
y2 = −4x.
The general formula for this parabola is y2 = 4px.
Therefore, the value of p is _____
The coordinates of the focus are ______
The equation of the directrix is ______
Answers
Answer:
The answers to your three problem question are shown
1) the value of p is
p = -1
2) The coordinates of the focus are
Focus = (-1,0)
3) The equation of the directrix is
Directrix
x = 1
Step-by-step explanation:
The general equation for this parabola is
y^2 = 4px
Problem 1
Find the value of p.
We are told that the equation of the problem is
y^2 = -4x
And the general formula is
y^2 = 4px
From there, we can deduce that
p = -1, because
y^2 = 4(-1)x = -4x
This means that p = -1
Problem 2
Find the focus
To find the focus we can see the equations attached below for the focus, vertex and directrix.
In these case, the equations still apply, even though the variable is inverted, we just need to adjust it
y^2 = -4x =>
x = (-1/4)*y^2
x = a*y^2 + b*y +c
Focus
((4ac -b^2 + 1)/4a, -b/2a)
But, b = 0 and c = 0
=>
(1/4a,0) = (1/4(-1/4),0) = (-1,0)
Focus = (-1,0)
Problem 3
Find the directrix
The equation is
x = c - (b^2 + 1).4a
But, b = 0 and c = 0
x = -4*a
x = -4* (-1/4) = 1
x = 1
Directrix
x = 1
Answer: P is -1
Focus is (-1,0)
Directrix is X= 1
Related Questions
Write as a complex number in standard form
Answers
Answer:
Complex numbers are numbers in which the real component and the imaginary part of the number are both represented. The numbers in standard form will be a + bi, where a is the real part and bi is the imaginary part. An example of a complex number would be 3 +5i. 3 is the real part, and 5i is the imaginary part.
Step-by-step explanation:
Hope this helps!
The complex number 3cis210 can be written in standard form as - (3√3/2)i - (3/2).
Explanation:The complex number 3cis210 can be written in standard form as:
3cis210 = 3(cos(210°) + i sin(210°))
Using the trigonometric identities cos(210°) = -√3/2 and sin(210°) = -1/2, we can simplify:
3cis210 = 3(-√3/2 + i(-1/2))
Therefore, the complex number 3cis210 in standard form is - (3√3/2)i - (3/2).
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The complete Question is given below:
Write as a complex number in standard form 3cis210
Convert the following measurements into the units given in the brackets
a. 8m (mm)
b. 0.02m (mm)
c. 110 000 mm (m)
d. 28 400 cm (km)
e. 0.00001km (cm)
f.62 743 000 mm (km)
g. 5cm (mm)
h. 2.8m (cm)
i . 521cm (mm)
j. 83.7cm (m)
k. 4.6 km (m)
l. 2170m (km)
Answers
b. 0.02m = 20mm
c. 110000mm = 110m
d. 28400cm = 0.284km
e. 0.00001km = 1cm
f. 62743000mm = 62.743km
g. 5cm = 50mm
h. 2.8m = 280cm
i. 521cm = 5210mm
j. 83.7cm = 0.837
k. 4.6km = 4600m
l. 2170m = 2.17km
write the standard equation of a circle with the center at (-1,-4) that passes through the point (-1,-1)
Answers
Answer:
(x+1)^2+(y+4)^2=9
Step-by-step explanation:
First equation in what I like to call center-radius form is (x-h)^2+(y-k)^2=r^2 where (h,k) is center and r is radius.
So we are given (h,k)=(-1,-4) so we have so far that
(x+1)^2+(y+4)^2=r^2
Passes through the point (-1,-1) means at some point (x,y) takes on the point (-1,-1) so guess what we are going to find r^2 by plugging in that point where x and y are.
(-1+1)^2+(-1+4)^2=r^2
(0)^2+(3)^2=r^2
9=r^2
so the equation of the circle is (x+1)^2+(y+4)^2=9
Answer:
(x + 1)² + (y + 4)² = 9
Step-by-step explanation:
The equation of a circle is:
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
The center is (h, k) = (-1, -4). The radius is the distance from the center to any point on the circle. (-1, -1) is 3 units above the center, so r = 3.
(x + 1)² + (y + 4)² = 9
Solve the equation x4 – 26x2 + 25 = 0 in the real number system.
Answers
Answer:
x = -1, 1, -5 , 5.
Step-by-step explanation:
x4 – 26x2 + 25 = 0
Factoring:
(x^2 - 25)(x^2 - 1) = 0
So x^2 - 25 = 0 gives x^2 = 25 and x = +/- 5.
x^2 - 1 gives x^2 = 1 and x = +/- 1.
Follow below steps:
To solve the equation x4 − 26x2 + 25 = 0, we can use substitution to simplify the equation. Let's set u = x2, which turns our equation into a quadratic form: u2 − 26u + 25 = 0.
Now, we apply the quadratic formula where a = 1, b = -26, and c = 25 to find the values of u. The quadratic formula is u = (-b ± √(b2 - 4ac))/(2a). Substituting the values, we get the roots for u which are u = 25 and u = 1.
Now we substitute back for x by setting x2 = u, which gives us two separate equations to solve: x2 = 25 and x2 = 1. Solving these, we find the solutions for x to be x = 5, x = -5, x = 1, and x = -1.
Plz help help me sombody help
Answers
Answer:
2/3
Step-by-step explanation:
We can find the slope of the line by using points
We have 2 points (-2,0) and (1,2)
Using the formula for slope
m = (y2-y1)/(x2-x1)
= (2-0)/(1--2)
= 2/(1+2)
= 2/3
What is the range of y =|3x + 1|?
Answers
Answer:
[0,∞), {y|y≥0}
Step-by-step explanation:
The graph of y =|3x + 1| is attached.
By observation, we can see that the the least y-value that the graph can take is y =0 (i.e the x-axis) and the greatest y-value that the graph can take is positive infinity.
Hence the range is [0,∞), {y|y≥0}
Final answer:
The range of the function y = |3x + 1| is [0, infinity), as absolute value functions always yield non-negative values.
Explanation:
The range of the function y = |3x + 1| can be determined by understanding the behavior of absolute value functions. The absolute value function |x| always yields a non-negative value. Therefore, for any real number x, |3x + 1| will also be non-negative. Hence, the range of y = |3x + 1| is [0, ∞), meaning that y can be any real number greater than or equal to zero.
Which equation is equivalent to
Answers
Answer:
Simplifying the equation:
[tex]\frac{2}{3} x - \frac{5}{6} = -\frac{5}{12} x + \frac{1}{4}[/tex]
Grouping like terms:
[tex]\frac{2}{3} x + \frac{5}{12} x= \frac{1}{4} + \frac{5}{6}[/tex]
⇒ [tex]\frac{39}{36} x=\frac{26}{24}[/tex]
Solving for 'x', we have:
⇒ [tex]x=\frac{26}{24}\frac{36}{39}=1[/tex]
For this case we place the terms with "x" on the left side of the equation, and the terms without "x" on the right side:
[tex]\frac {2} {3} x + \frac {5} {12} x = \frac {1} {4} + \frac {5} {6}[/tex]
We add similar terms:
[tex]\frac {24 + 15} {36} x = \frac {6 + 20} {24}\\\frac {39} {36} x = \frac {26} {24}[/tex]
We simplify both sides:
[tex]\frac {13} {12} x = \frac {13} {12}[/tex]
Dividing by [tex]\frac {13} {12}[/tex] on both sides of the equation:[tex]x = 1[/tex]
Answer:
[tex]x = 1[/tex]
Given that (5,4) is on the graph of f(x), find the
corresponding point for the function
f(x) + 4.
Answers
Answer:
(5, 8)
Step-by-step explanation:
f(x) + 4 is the graph of f(x) translated 4 units vertically up
given (5, 4) is a point on f(x), then the coordinates of the corresponding point
x- coordinate remains unchanged and add 4 to the y- coordinate
The corresponding point on f(x) + 4 is (5, 4 + 4) = (5, 8)
Which of the following equations represents a line that is perpendicular to
y = -4x+9 and passes through the point, (4, 5)?
A. y- x+5 B. y- *x+6
C. y = x+4 D. y --4x+4
Answers
For this case we have that if two lines are perpendicular, then the product of their slopes is -1.
If we have the following equation of the line:
[tex]y = -4x + 9[/tex]
The slope is [tex]m_ {1} = - 4[/tex]
Then yes:
[tex]m_ {1} * m_ {2} = - 1\\m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- 4}\\m_ {2} = \frac {1} {4}[/tex]
The equation of the new line will be:
[tex]y = \frac {1} {4} x + b[/tex]
We substitute the point to find "b":
[tex]5 = \frac {1} {4} (4) + b\\5 = 1 + b\\b = 5-1\\b = 4[/tex]
Finally, the equation is:
[tex]y = \frac {1} {4} x + 4[/tex]
Answer:
[tex]y = \frac {1} {4} x + 4[/tex]
Mr.santos plants beans and squash in the area shown in the model below which expression is equivalent to the sum of the two areas?
Answers
Answer:
I would go with A. 3(4 + 7) acres
Step-by-step explanation:
Easy, the expression is equivalent to the sum of two areas... Beans and the Squash... you just add them all together and you get 33 acres. Add the parenthesis first and then multiply by 3 you get 33
Answer:
the answer is 3(4+7
Step-by-step explanation:
Fill in the blank.in the triangle below,z degrees=___
Answers
Answer:
Z°= 88.36
Tan-1×35=88.36
Answer:
z = 38 degrees
Step-by-step explanation:
As we can see in the picture that the triangle is a right angle triangle and two of the angles are known.
We also know that the sum of internal angles of a triangle is 180 degrees.
We know that one angle is 90 degrees and second is 52 degrees.
So,
Sum of three angles = 180 degrees
90 + 52 + z = 180
z = 180 - 90 - 52
z = 38 degrees ..
Simplify the following expression.
Answers
Answer:
B.
Step-by-step explanation:
It is just common sense. The top numbers have to be smaller than the top numbers
What is the value of x?
Answers
Answer: x = 7
`Step-by-step explanation:
Because the figure shows two triangles that are similar. we can write and solve an equation of ratios:
9 cm 72 cm
----------- = -----------
3x - 20 56 cm
Cross-multiplying, we get (3x - 20)(72 cm) = (9 cm)(56 cm) = 504 cm²
Dividing both sides by 72 cm, we get:
3x - 20 = (504 cm²) / (72 cm) = 7
Then 3x - 20 = 7, and 3x = 27. Then x must be 9.
The value of x in the triangle with parallel lines is 9.
To find the value of x in the equation involving a triangle with parallel lines, we can start by simplifying the equation and then solve for x.
The given equation is:
9/72 = (3x - 20)/56
Let's first simplify the left-hand side of the equation:
9/72 = 1/8
Now, the equation becomes:
1/8 = (3x - 20)/56
To isolate x, we can cross-multiply:
1 * 56 = 8 * (3x - 20)
56 = 24x - 160
Next, add 160 to both sides of the equation:
56 + 160 = 24x
216 = 24x
Finally, divide both sides by 24 to solve for x:
x = 216/24
x = 9
So, the value of x in the given equation is 9.
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For the following system, use the second equation to make a substitution for y in the first equation.
2x + y = 5
y + 3 = 2x
2x + 2x - 3 = 5
2x + 3 - 2x = 5
2x + 2x + 3 = 5
Answers
Answer:
It is A
Step-by-step explanation:
2x + y = 5
y + 3 = 2x
From equation 2:
y = 2x - 3
Substituting in the first equation:
2x + 2x - 3 = 5.
Answer:
2x + 2x - 3 = 5.
Step-by-step explanation:
Find the sum
3a/bc+2b/ac
Answers
Answer:
3a^2 + 2b^2
= ----------------------
abc
Step-by-step explanation:
3a 2b
------- + ----------
bc ac
3a^2 + 2b^2
= ----------------------
abc
X+y-3z=8
Slove for x
Answers
x= −y + 3z +8
[tex]x+y-3z=8\\x=-y+3z+8[/tex]
A scientist is trying to determine whether the use of cell phone contributes to brain cancer. For his study, he compares the medical records of subjects who have been diagnosed with brain cancer to the records of healthy subjects. What is the most significant weakness in this type of study?
The test groups must be unusually large to generate significant data.
The relationship between cell phone use and cancer is difficult to determine.
This type of study is expensive, and the data are difficult to analyze.
This type of study must rely on medical records, which are inaccurate.
Answers
Answer:
The relationship between cell phone use and cancer is difficult to determine.
Step-by-step explanation:
Its pretty difficult to determine the relationship between using your phone and cancer, and how they correspond to each other.
Answer:
The relationship between cell phone use and cancer is difficult to determine.
Step-by-step explanation:
There has been always a conflicting conclusions whether there is a relationship between a cell phone and the cause of brain cancer. Many years of studies by the scientist and the neurologist on the relation on cellphones and cancer have resulted in controversial arguments.
Thus, the most significant weakness in this type of study is the relationship between cell phone use and cancer is difficult to determine.
The endpoints of a regular pentagon are (-1,4) and (2,3). What is the perimeter of the Pentagon?
1. Square root of 10
2. 5 square root of 10
3. 5 square root of 2
4. 25 square root of 2
Answers
the assumption being that the endpoints are two continuous points in the pentagon, Check picture below.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2-(-1)]^2+[3-4]^2}\implies d=\sqrt{(2+1)^2+(3-4)^2} \\\\\\ d=\sqrt{9+1}\implies d=\sqrt{10}~\hfill \stackrel{\stackrel{~\hfill \stackrel{\textit{5 sides}}{}}{\textit{perimeter of the pentagon}}}{5\sqrt{10}}[/tex]
If you divide-16 in 5 equal parts how much is each part equal to
Answers
Answer:
-3.2
Step-by-step explanation:
coven 12 - 31:1-13; wees laula
Iven
WILL GIVE BRAINLIEST PLEASE HELP
Answers
True or false? In a mapping diagram, a relation that is a function can have two arrows coming from the same input value.
Answers
Answer:
false
Step-by-step explanation:
In a mapping diagram, a relation that is a function can have two arrows coming from the same input value
false
Answer: False.
Step-by-step explanation:
By definition, a relation is a function if each input value has only one output value.
Knowing this, we can say that in a mapping diagram, a function will never have two arrows coming from the same input value.
In other words, if in a mapping diagram a relation has two arrows coming from the same input value, this means that this input value has two output values, and according to the definition mentioned above, this relation cannot be a function.
Therefore, the statement "In a mapping diagram, a relation that is a function can have two arrows coming from the same input value", is FALSE.
I need help please :’( Simplify -4x - x
Answers
Answer:
-5x
Step-by-step explanation:
Answer:
-5x
Step-by-step explanation:
-4x-x --------------> factor out the x
= (-4-1) x
= -5x
In simplified form, V18 is
Answers
Answer: 4.24264069
Step-by-step explanation: I think you mean the square root?
How do I find the value of x if y=70?
Answers
x would be 70 too.
Here’s how.....
According to the Opposite Inverted Angles rule, this would be the case.
It is Opposite Inverted Angles because of the 2 straight lines that creates the cross section.
Hopes it helps
If 2x + y = 6 and m - n = 2, what is the value of (4x + 2y)(4m - 4n)
Answers
Answer:
96
Step-by-step explanation:
If m - n = 2, then 4m - 4n = 4(m - n) = 4(2).
Then (4x + 2y)(4m - 4n) equals (4x + 2y)(8), or 8(4x + 2y).
But we are told that 2x + y = 6. Multiplying all terms by 2, we get
4x + 2y = 12. Substituting 12 for 4x + 2y, we get our final answer:
(4x + 2y)(4m - 4n) equals (4x + 2y)(8), or 8(4x + 2y), or 8(12) = 96
Answer:
96
Step-by-step explanation:
(4x + 2y)(4m - 4n) = ?
We have an equation
2x+y =6
Multiply it by 2
2(2x+y) = 2*6
Distribute
4x+2y = 12
Substitute 12 in for 4x+2y into the original problem
12(4m - 4n) = ?
We have an equation
m-n = 2
Multiply this by 4
4(m-n) = 4*2
Distribute
4m-4n = 8
Substitute 8 in for 4m -4n in 12(4m - 4n) = ?
12 * 8 = ?
96
If the slope of GH is −4/5 and the slope of HJ is 3/4, find the slope of JK so that GHJK is a parallelogram. quick answer pls
Answers
Answer:
Slope of JK = -4/5
Step-by-step explanation:
We know that GHJK is a parallelogram. If GHJK is a parallelogram then the sides of parallelogram will be:
GH, HJ, JK, GK
Hence the opposite sides will be:
GH and JK
HJ and GK
We know that opposite sides of parallelogram are parallel to each other and the slopes of parallel lines is equal.
So the slope of GH and JK will be equal.
And slopes of HJ and GK will be equal.
As we are given the slope of GH which is -4/5, the slope of JK will also be -4/5 because both lines are parallel.
Identify the pairs of rates as equivalent or not equivalent.
Tiles
18/3 and 9/1
32/4 and 8/1
36/6 and 6/1
20/5 and 3/1
35/7 and 5/1
100/10 and 5/1
Boxes
Equivalent pairs
Not Equivalent pairs
Answers
ANSWER
See explanation
EXPLANATION
If we can simplify the first fraction to obtain the second fraction, then the two fractions are equivalent pairs
EQUIVALENT PAIRS
[tex] \frac{32}{4} \: and \: \frac{8}{1} [/tex]
[tex]\frac{36}{6} \: and \: \frac{6}{1} [/tex]
[tex]\frac{35}{7} \: and \: \frac{5}{1} [/tex]
NOT EQUIVALENT PAIRS
[tex]\frac{18}{3} \: and \: \frac{9}{1} [/tex]
[tex]\frac{20}{5} \: and \: \frac{3}{1} [/tex]
[tex]\frac{100}{10} \: and \: \frac{5}{1} [/tex]
Answer:
Equivalent pairs
32/4 and 8/1
36/6 and 6/1
35/7 and 5/1
Not Equivalent pairs
18/3 and 9/1
20/5 and 3/1
100/10 and 5/1
Step-by-step explanation:
Equivalent pairs: Those pairs that are different fractions but represent the same number.
1. 18/3 and 9/1
18/3 can be simplified into 6/1
so, 18/3 and 9/1 are not equivalent pairs
2. 32/4 and 8/1
32/4 can be simplified into 8/1
so, 32/4 and 8/1 are equivalent pairs
3. 36/6 and 6/1
36/6 can be simplified into 6/1
so, 36/6 and 6/1 are equivalent pairs
4. 20/5 and 3/1
20/5 can be simplified into 4/1
so, 20/5 and 3/1 are not equivalent pairs
5. 35/7 and 5/1
35/7 can be simplified into 5/1
so, 35/7 and 5/1 are equivalent pairs
6. 100/10 and 5/1
100/10 can be simplified into 10/1
so, 100/10 and 5/1 are not equivalent pairs
circle o has a circumfrence of approximately 44 in. what is the approximate lenght of the diameter d?
-7in
-14in
-22in
-44in
Answers
Answer:
14 inch
Step-by-step explanation:
formula for circumference:
2(pi)r @ (pi)d
*where: r = radius
d= diameter
pi used = 22/7
22/7 x d = 44
d= 44/ (22/7)
=14
Please help!!! Which is not equal to the others?
Answers
Answer:
b
Step-by-step explanation:
Given
a cos2x
b
2sinxcosx = sin2x
c
2cos²x - 1 = cos2x
d
1 - 2sin²x = cos2x
b is the expression not equal to the others
---------------------------------------------------------------------------
Note
cos2x = cos²x - sin²x = cos²x - (1 - cos²x) = 2cos²x - 1
cos2x = (1 - sin²x) - sin²x = 1 - 2sin²x
The solution to the system of equation below is (−2, −1).
2x − 3y = −1
11x − 9y = −13
When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10.
Which system of equations will also have a solution of (−2, −1)?
Answers
Answer:
x = -2, y = -1 → (-2, -1)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x-3y=-1&\text{multiply both sides by (-3)}\\11x-9y=-13\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-6x+9y=3\\11x-9y=-13\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=-10\qquad\text{divide both sides by 5}\\.\qquad x=-2\\\\\text{put the value of x to the first equation:}\\\\2(-2)-3y=-1\\-4-3y=-1\qquad\text{add 4 to both sides}\\-3y=3\qquad\text{divide both sides by (-3)}\\y=-1[/tex]
Answer:
A on edge
Step-by-step explanation: