We can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:
The parabola is a vertical parabola and facing up.The vertex of the parabola is v(-8, 0).p value of the parabola is 1.A parabola refers to the shape that traces the equation of the form ax² + bx + c.
A parabola's directrix is a vertical or horizontal line that never contacts the parabola and is located at p distance from the vertex and 2p distance from the focus.
The parabola created when the directrix is on the y coordinate called a vertical parabola.
If the directrix value is greater than the corresponding focus or vertex, there will be a negative p and the parabola will face downhill.
If the directrix value is less than the corresponding focus or vertex, there will be positive p and the parabola will face up.
From the given definition of the directrix, we can find the value of p;
2p = y coordinate of focus - equation of the directrix
2p = 1 - (-1)
2p = 2
p = 1
Vertex, v(h, k) compared with f(h, k + p), we will get;
k + p = 1
k = 0
Therefore, the vertex is (-8, 0).
Thus, we can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:
The parabola is a vertical parabola and facing down.The vertex of the parabola is v(-8, 0).p value of the parabola is 1.To learn more about directrix of a parabola visit:
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During one month andre used 785 gallons of water at his home. There are approximately 3. 8 liters in 1 gallon. Which measurement is closest to the number of liters andre used during this month?.
Andre used 2983 gallons of liquid all through this month.
Given;
Andre used 785 gallons of water at his house in a single month. In a gallon, there are roughly 3.8 liters.
To get the measurement that is closest to the number of liters Andre used during this month;
The total gallons of water used in a month = 785 gallons
The quantity of water in a single gallon = 3.8 liters
Therefore, the number of liters Andre used during this month;
U = total gallons of water used in a month * quantity of water in a single gallon
U = 785 * 3.8
U = 2983
Hence, the number of liters Andre used during this month is 2983 gallons.
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Help me with this question
Point A, C and F lies on the given line y = [tex](\frac{1}{4} )^{x}[/tex] .
Given in question,
y = [tex](\frac{1}{4} )^{x}[/tex]
y = [tex]4^{-x}[/tex]
Points A(-2,16), B(2,8), C(-1,4), D(0,4), E(1,4), F(0,1) and G(-2,0)
We will points in the equation.
For point A(-2,16)
[tex]16 = 4^{-(-2)}[/tex]
[tex]= 4^{2}[/tex]
[tex]16=16[/tex] True
For point B(2,8)
[tex]8= 4^{-2}[/tex]
[tex]=\frac{1}{4^{2} }[/tex]
[tex]=\frac{1}{16}[/tex]
[tex]8=\frac{1}{16}[/tex] False
For point C(-1,4)
[tex]4=4^{-(-1)}[/tex]
[tex]=4^{1}[/tex]
[tex]4=4[/tex] True
For point D(0,4)
[tex]4=4^{-0}[/tex]
[tex]4= 1[/tex] False
For point E(1,4)
[tex]4=4^{-1}[/tex]
[tex]4=\frac{1}{4}[/tex] False
For point F(0,1)
[tex]1=4^{-0}[/tex]
[tex]1=1[/tex] True
For point G(-2,0)
[tex]0=4^{-(-2)}[/tex]
[tex]= 4^{2}[/tex]
[tex]0=16[/tex] False
Hence, only point A,C and F satisfies the equation.
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PLEASE HELP!
Simplify the expression to a + bi form:
√25 + √-81 + √25 - √-16
Answer:
10 + 5i
Step-by-step explanation:
[tex] \rm \implies \sqrt{25} + \sqrt{ - 81} + \sqrt{25} - \sqrt{ - 16} \\ \\ \rm \implies 5 + 9i + 5 - 4i \\ \\ \rm \implies 10 + 5i[/tex]
There are 163 students going on a field trip to pan for gold.
If they are going in vans that hold 9 students each, how many vans are needed? How many students will ride in the van that isn't full?
Please answer and thank you
Answer:
Step-by-step explanation:
18 Vans. That will hold 162 Students if 9 student per Van
19 Vans since we need 163.
Answer: 19 Vans, and All but one will be full the one that isn't full holds one Student.
In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?
For the given triangle, its greatest possible perimeter is 45 cm.
What is the perimeter?The term perimeter has to do with the distance round on object. In this case we do have a triangle and the triangle has three sides. The perimeter of the triangle would be the distance round the triangle.
From the statements we have;
Third side = 15
second side = x
first side = 3x
Then;
x + 15 > 3x
15 > 3x - x
15> 2x
x < 7.5
Thus;
For the first side; 3 * 7.5 = 22.5
For the second side = 7.5
Third side = 15
Greatest possible perimeter of the triangle = 22.5 + 7.5 + 15
= 45 cm
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A square and rectangle are shown below. The width of the rectangle is the same as
the length
of a side of the square, both represented by .x. The length of the rectangle is one
foot more
than twice its width. The perimeter of the rectangle is 26 feet more
than that of the square.
(a) Write an expression for the length of the rectangle in
terms of.x. Label on the drawing.
x
Answer:
Step-by-step explanation:
x=26
Yolanda got a prepaid debit card with$20 on it. For her firt purchae with the card, he bought ome bulk ribbon at a craft tore. The price of the ribbon wa 16 cent per yard. If after that purchae there wa $12.32 left on the card, how many yard of ribbon did Yolanda buy?
Answer:
Yolanda bought 48 yards of ribbon, and spent 7.68 cents on it.
Step-by-step explanation:
First Step: Find out how much Yolanda spent
20.00 -12.32 = 7.68
Second Step: Divide Total Cost by Price of one Yard
7.68/0.16 = 48
Third Step: Double Check
48 x 0.16 = 7.68
I hope my answer helped you, good luck on your homework!
What is the sum of (3x + 4) + (9x – 10)?
Answer:
[tex]12x -6[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
1.209, 1.9, 3.76, 1.29 order these numbers from least to greatest
Answer:
1.209 < 1.29 < 1.9 < 3.76
Step-by-step explanation:
in 4 and 5, find each sum. Use fraction
to help.
4. 1/2 + 2/5 = 9/10 + =
what is they intercept of this quadratic function? f(x) = -x2 + 10x - 22
Answer:
(0,-22)
Step-by-step explanation:
Plug in 0 for x and solve for y
Rewrite in simplest terms: (-10x+2)+(-9x+8)
The simplest form of the given expression is -19x + 10.
The process or product of making something less complicated and thus easier to do or understand is called simplification. Replace 'of' with 'Multiplication' and '/' with 'Division.' Always perform operations in the order specified by 'BODMAS.' Division and multiplication are both given equal weight (Starting from left) Subtraction and addition have the same.
Given that
(-10x+2) + (-9x+8)
We have to simplify the given expression
= -10x + 2 - 9x + 8
= (-10x - 9x) + (2 + 8)
= -19x + 10
Therefore the simplest form of the given expression is -19x + 10
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Please help me please
Answer:
16.53
Step-by-step explanation:
Start by finding the length of the line in the center. I will call this line a. Using the Pythagorean Theorem with 12.3 as the hypotenuse:
[tex]c^2=a^2+b^2\\a=\sqrt{c^2-b^2} \\a=\sqrt{12.3^2-5.4^2} \\a=\sqrt{122.13} \\a=11.05[/tex]
Now that this line is known, x can be found. Once again using the Pythagorean Theorem:
[tex]x^2=a^2+b^2\\x=\sqrt{a^2+b^2} \\x=\sqrt{12.3^2+11.05^2} \\x=\sqrt{273.39} \\x=16.53[/tex]
643251 to the nearest then thousands
Answer:
64000
Step-by-step explanation:
When you are rounder you must look at the last number to determine if you are rounding up or down.
Write the first 4 terms of the sequence defined by the given rule.
4. f(n) = n³-1
The first four terms of the sequence defined by the rule f(n) = n³-1 are -1, 0, 7 and 26.
According to the question,
We have the following expression:
f(n) = n³-1
Now, in order to find the first four values of the given expression, we will change the values of n from 0 to 3.
So, putting the value of n as 0, we have:
f(0) = 0³-1
0-1 = -1
Now, putting the value of n as 1, we have:
1³-1
1-1
0
Now, putting the value of n as 2, we have:
2³-1
8-1
7
Now, putting the value of n as 3, we have:
3³-1
27-1
26
Hence, the first four terms of the sequence defined by the rule f(n) = n³-1 are -1, 0, 7 and 26.
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find the perimeter and area
Answer:
perimeter = 22 km and area = 18 km^2
Step-by-step explanation:
First I found and labeled the missing lengths. For the one at the top of the shape, I added 1 + 2 + 3 to get the length, since those are what make up the length.
Afterwards I just added up all the side lengths to get the perimeter. 2+6+2+3+2+3+1=22, so the perimeter is 22 km.
To find the area, I split the shape into two, labeled 1 and 2. (Check the image attached) To find the area you multiply length by width, so i did that for shapes 1 and 2. For shape 1, I did 2 x 6 and got 12, and for shape 2 I did 3 x 2 to get 6. To get the total area of the entire shape, add these two areas. 12 + 6 = 18, so the total area is 18 km^2. (km squared)
let me know if anything is confusing :-))
Which method and additional information would prove δonp and δmnl similar by the aa similarity postulate? segments om and lp intersect at point n; triangles are formed by points lnm and onp; line k intersects with both triangles at point n. use a rigid transformation to prove that ∠opn ≅ ∠mln. use rigid and nonrigid transformations to prove segment pn over segment mn = segment ln over segment on. use a rigid transformation to prove that ∠npo ≅ ∠lnm. use rigid and nonrigid transformations to prove segment ln over segment on = segment pn over segment mn.
The correct option for the method and additional information that would prove triangle ONP and triangle MNL similar by AA similarity postulate is
option B.
B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.
Angle Angle AA similarity postulate states that two triangles are similar if : two angles in one of the triangles are congruent (equal) to two angles in the other triangle.
The reason for arriving at the above selection is as follows:
The known parameter in triangle ΔONP and ΔMNL are;Lines MO and LP intersect at vertex point N.The angles on opposite side of the point N (either side of the X shape formed by the two lines) which are ∠ONP and ∠LNM are vertically opposite angles or opposite angles.According to vertically opposite angles theorem ∠ONP and ∠LNM, which are vertically opposite angles are congruent, and we can write.
∠ONP ≅ ∠LNM
The required parameters are:
To find the additional information that would prove ΔONP and ΔMNL by
AA (Angle-Angle) similarity postulate.
Given from the drawing,
One (vertex) angle in one triangle is congruent to one (vertex) angle in the other triangle, that is ∠ONP ≅ ∠LNM, it is required to prove that one other angle in triangle ΔONP is congruent to a corresponding angle in triangle ΔMNL.
Prove that:
either ∠NPO or ∠NOP in ΔONP are congruent to ∠NLM or ∠NML respectively in ΔMNL by performing rigid transformations (transformations that does not change shape) on either ΔONP or ΔMNL including:
Rotating triangle ΔONP by 180° with origin at point N, to form the image ΔO'N'P'.
Translating the vertex point P' in the image ΔO'N'P', to the location of the point L in ΔMNL, and verify that the segments LN and LM in ΔMNL coincide with the segments P'N' and P'O' respectively of triangle ΔO'N'P'.
Therefore, the correct option is option B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.
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Answer:
b
Step-by-step explanation:
Expression that equal to p/6+(q+8)
Answer: (p/6 + q) + 8
Step-by-step explanation:
2/3+____=5/6 what Is the answer
Answer: 2/3+ 1/6
Step-by-step explanation: 2/3= 4/6 4/6 + 1/6 = 5/6
bju pre algebra homework, due tomorrow. (please dont do questions 1-6)
SUPER EASY ASAP !!!!!!
The function f (x) has steeper slope.
So, The Paige is correct.
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The input output pairs of f (x) are (- 6, 5/2) and (- 1, 17/2)
And, The input output pairs of g (x) are (2, 13/3) and (6, - 1)
Now,
Find the slope for f (x) as;
m₁ = (17/2 - 5/2) / (- 1 - (-6))
m₁ = (15/2) / 5
m₁ = 15/10
m₁ = 3/2
And, Slope for g (x) is;
m₂ = (- 1 - 13/3) / (6 - 2)
m₂ = (- 16/3) / 4
m₂ = - 16 / 12
m₂ = - 4 / 3
Thus, The function f (x) has steeper slope.
So, The Paige is correct.
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Triangle DOG i an iocele with bae angle D and G. Line egment DO i one more than the quare of a number, and line egment OG i two le than four time a number. Line egment DG i three le than twice the number. Find the number, the length of the leg, and the length of the bae
Answer:
the number is 3DO = OG = 10DG = 3Step-by-step explanation:
Given isosceles triangle DOG with DO≅GO, DO = (n²+1), GO = (4n-2) and DG = (2n -3), you want the value of n and the lengths of the sides.
SetupThe expressions for the congruent sides will have the same value, so ...
DG -GO = 0
(n² +1) -(4n -2) = 0
Solutionn² -4n +3 = 0 . . . . . . . . simplify
(n -3)(n -1) = 0 . . . . . . factor
n = 1 or 3 . . . . . . . . values of n that make the factors zero
The length of leg DG is ...
2n -3 = 2{1, 3} -3 = {2, 6} -3 = {-1, 3}
Side DG cannot be negative, so the "solution" n = 1 is extraneous.
GO = 4n -2 = 4(3) -2 = 10
The number is 3, the leg lengths are DO = OG = 10, and the base length is DG = 3.
Write the equation of a line that is perpendicular
to -y = -x and contains point (−1,−1)
Answer:
y = - x
Step-by-step explanation:
-y = -x is the same as y=x and to get an equation that is perpendicular to another one you just have to find the reciprocal (opposite) number of the SLOPE. The reciprocal of 1 is -1, therefore the perpendicular equation to -y=-x is y=-1
0.96 in fracton form
Answer:
As a fraction in simplest form it SHOULD be 24 over 25.
Step-by-step explanation:
"0.96 as a fraction (simplified form)" MagnetsAndMotors (Dr. B's Other Channel)
Answer:
24/25
Step-by-step explanation:
0.96
By counting the numbers after the decimal point which is two.
so we will write: 96/100, since hundred has to two zero.
Then we will divide 96/100 to it simplest form which is 24/25
you want to estimate the proportion of students at your university in favor of a longer spring break. changing the confidence level from 95% to 90% will decrease the needed sample size if the margin of error . please choose the correct answer from the following choices, and then select the submit answer button. answer choices
The needed sample size Smaller if the margin of error .
Given,
In the question:
This question in the form of: Fill in the blanks.
So, You want to estimate the proportion of students at your university in favor of a longer spring break. changing the confidence level from 95% to 90% will decrease the needed sample size_____ if the margin of error.
Hence, The answer is smaller the margin of error.
Let's Know:
What is Confidence level?
The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way. The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.
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How many minutes are in 1 hour and 3/4? How do you solve it as well?
Answer:
Step-by-step explanation:
105 min
60 min in a hour and then 3/4 of a hour is 45 min.
Total: 105 minutes
A helicopter hovers 60 m above the ocean's surface. A submarine is resting 30 m
underwater, directly below the helicopter. What is the difference between the positions of these two objects?
Answer:
90 m
Step-by-step explanation:
because the helicopter is 60 m up and the submarine is 30 m under so combining the two helps us identify the difference between the two objects
Solve for x in the equation x + 9 = −25. −34 −16 25 34 NEED HELP ASAAAAAAAPPPP
I need help please!!!
Please help me I really need help
Answer:
No
Step-by-step explanation:
parallel is when 2 lines never touch and move in the same direction and these touch and move in different directions
Hopes this helps please mark brainliest