Answers
The equation of the parabola having focus (1,1) and directix y = -1 is
y = x²/4 - x/2 + 1/4
The focus of the parabola (h , k + p) = (1,1)
The directrix of the parabola is y = -1
From, the focus
k + p = 1
k = 1 - p
The formula of directrix is
y = k - p (1)
Substituting the value of directrix and k
-1 = 1 -p -p
-1-1 = -2p
-2 = -2p
p = 1
Substituting the value p in equation (1)
k = 0
Now, we have got the vertex of the parabola (h ,k) is (1,0)
The equation of the parabola is
(x-h)² = 4p (y - k)
(x - 1)² = 4 (1) (y - 0)
( x -1 )² = 4(y )
x² - 2x + 1 = 4y
x²/4 - 2x/4 + 1/4 = y
y = x²/4 - x/2 + 1/4
which is the equation of the parabola.
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Related Questions
13. A number line is shown below. Which of the following expressions represents the distance between -4and 5 on the number line?-4-3-2-1012345A. 1-4+51B. 14-51C. |-5-(-4)D. |-4-51
Answers
Remember that to find a distance between two numbers, we have to subtract the least number from the greater one. So, in this case, we have -4 and 5, where 5 is greater than -4.
[tex]5-(-4)=5+4=9[/tex]Therefore, the distance between the numbers is 9.The answer is C.SO GUYSS I NEED THIS TODAY if it not to much to ask for.....
how does simple interest show proportional reasoning and relate to the percent equation
Answers
Answer: Use cross-product to determine if the two ratios form a proportion.
(1/8) raised to -x ppwer= 64 raised to x powerI'll upload a picture
Answers
x = 0
Explanation:[tex](\frac{1}{8})^{-x}=64^x[/tex][tex]\begin{gathered} \frac{1}{8\text{ }}\text{ = }\frac{1}{2^3}\text{ } \\ \text{Rule: }\frac{1}{a^b}=a^{-b} \\ so,\text{ }\frac{1}{2^3}=2^{-3} \\ (\frac{1}{8\text{ }})^{-x}=(\frac{1}{2^3})^{-x}\text{ = }(2^{-3})^{-x} \\ =2^{3x} \end{gathered}[/tex][tex]\begin{gathered} 64=2^6 \\ 64^x=(2^6)^x=2^{6x} \\ (\frac{1}{8})^{-x}=64^x \\ 2^{3x}\text{ = }2^{6x} \\ \text{base cancels out:} \\ 3x\text{ = 6x} \end{gathered}[/tex][tex]\begin{gathered} 3x\text{ - }6x\text{ = 0 } \\ -3x\text{ = 0} \\ \text{divide both sides by -3:} \\ \frac{-3x}{-3}\text{ = }\frac{0}{-3} \\ x\text{ = 0} \end{gathered}[/tex]For the following exercise graph the given ellipse, noting center, vertices, and foci #41
Answers
Given the equation of an ellipse: #41
[tex]x^2+8x+4y^2-40y+112=0[/tex]To find the center and the vertices, we will complete the square of (x) and (y):
[tex]\begin{gathered} x^2+8x+4(y^2-10y)=-112 \\ (x^2+8x+16)+4(y^2-10y+25)=-112+16+100 \end{gathered}[/tex]Factor for (x) and (y) then simplify:
[tex]\begin{gathered} (x+4)^2+4(y-5)^2=4\rightarrow(\div4) \\ \\ \frac{(x+4)^2}{4}+\frac{(y-5)^2}{1}=1 \end{gathered}[/tex]The general form of the ellipse will be:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Comparing the equation with the form:
[tex]\begin{gathered} (h,k)=(-4,5) \\ a=\sqrt[]{4}=2 \\ b=\sqrt[]{1}=1 \\ c=\pm\sqrt[]{a^2-b^2}=\pm\sqrt[]{4-1}=\pm\sqrt[]{3} \end{gathered}[/tex]The graph of the ellipse will be as shown in the following picture:
As shown in the figure:
The center C = (h,k) = (-4 , 5)
The vertices denoted by V = (-6, 5) and (-2, 5)
Foci denoted by F =
[tex](-4+\sqrt[]{3},5),(-4-\sqrt[]{3},5)[/tex]40% of the airplanes were hydroplanes. If 660 were hydroplanes, how many were not hydropons?
Answers
40% of the airplanes were hydroplanes.
If 660 were hydroplanes, how many were not hydroplanes?
SOLUTION
If 40% of the airplanes were hydroplanes.
Let x represents the total number of Hydroplanes.
So that 40 % of X = 660
40/ 100 x X = 660
2 / 5 x X = 660
2X / 5 = 660
cross- multiply, we have:
2X = 660 X 5
2 X = 3300
Divide oth sides by 2 , we have :
X = 3300 / 2
X = 1650
Total number of Hydrophones = 1650
Those that are Hydrophones = 660
Those that are not Hydrophones = 1650 - 660
= 990
f(x) = -x +2^x+8
Find f(-2)
Answers
Value of f(-2) is 12.25.
What is equation?Equation, also known as a statement of equivalence between two expressions with variable- and/or number-based components. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Given Data
Expression
f(x) = -x +2ˣ+8
f(-2)
Equating -2 in the place of x
= -(-2) + 2⁻² + 8
= 4 + 8 +[tex]\frac{1}{4}[/tex]
= [tex]\frac{16+32+1}{4}[/tex]
= [tex]\frac{49}{4}[/tex]
= 12.25
Value of f(-2) is 12.25.
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15. The area of a triangle is given by
A = 1/2bh, where b is the base and h is the height of the triangle. In the triangle PQR above, PR=6, PQ=7, QR=12, and PH=3. If PH is perpendicular to QR, what is the area of the triangle PQR?
(A) 12
(B) 18
(C) 36
(D) 42
Answers
The answer is (B) 18.
In order to calculate the area of a triangle we must use the equation 1/2·base·height.
In this case, the base of the triangle would be QR, which is 12. The height would be PH, which is 3.
Using the formula above, we can do 1/2·12·3 which equals 18. This is the area of triangle PQR and our final answer.
Hope this helps.
Point M is the midpoint of AB¯¯¯¯¯. AM=2x+9, and AB=8x−50.
What is the length of AM¯¯¯¯¯¯?
Answers
Answer:
43
Step-by-step explanation:
→ Set up an equation
2x + 9 = 0.5 ( 8x - 50 )
→ Simplify
2x + 9 = 4x - 25
→ Minus 4x from both sides
-2x + 9 = -25
→ Minus 9 from both sides
-2x = - 34
→ Divide both sides by -2
x = 17
→ Substitute into AM
2 × 17 + 9 = 34 + 9 = 43
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
For the given question,
Figure A and D are the cases of reflection over y and x axis respectively.
What is termed as Translation?In mathematics, a translation is the movement of a shape to the left or right and/or upward or downward. The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions.For the given question,
Figure B and C are the cases of translation 3 right and 4 down respectively.
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If it laptop computer right now because $1549 and is on sale for $1149 what percentage discount is being given round your answer to the nearest hundredth when necessary
Answers
Okay, here we have this:
Considering the following equation:
Sale Price=Original Price*(100%-Percentage discount)
Replacing we obtain:
$1149=$1549*(100%-Percentage discount)
$1149/$1549=(100%-Percentage discount)
0.7417=100%-Percentage discount
Percentage Discount=100%-0.7417
Percentage Discount=1-0.7417
Percentage Discount=0.2583
Percentage Discount=25.83%
Finally we obtain that the discount percentage is 25.83%.
Multiplying Binomials with Fractional Coefficients
Express the product of (2x + 3) and (x − 3) as a trinomial in simplest form
Answers
[tex] = (2x + 3)(x - 3) \\ = 2x(x - 3) +3 (x - 3) \\ = 2 {x}^{2} - 6x + 3x - 9 \\ = 2 {x}^{2} - 3x - 9[/tex]
ATTACHED IS THE SOLUTION
5. Suppose that 25 acres of land is purchased, but because of roads and wetland concerns, 6 2/3 acres can not be developed into lots. How many 5/6 acre lots can the rest of the land be divided into?
Answers
22 lots of 5-6 acres each can be created from the remaining area.
What is acres?
The imperial and US customary systems both utilise the acre as a unit of land area. One chain by one furlong (66 by 660 feet) is the traditional definition, which is exactly equal to 10 square chains, 1/640 of a square mile, 4,840 square yards (43,560 square feet), and 4,047 m² (or around 40% of a hectare). An acre may be stated to be exactly 4,046.8564224 square metres based on the international yard and pound agreement of 1959.
Out of 25 acres of land 6 2/3 acres can not be developed into lots.
Therefore land that is left = 25 - 6 2/3 acres
= 25 - 20/3 acres
= 55/3 acres
No.of 5/6 acre lots can the rest of the land be divided into = 55/3 / 5/6 lots
= 22 lots
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What is 80% of 45?
WITH EXPLINATION PLS!!
Answers
Answer: The 80% of 45 is 36
Step-by-step explanation:
Write 80% as
80
100
Since finding the fraction of a number is the same as multiplying the fraction with the number, we have
80
100
of 45 =
80
100
× 45
Therefore, the answer is 36
If you are using a calculator, simply enter 80÷100×45 which will give you 36 as the answer. Hope it helps!
Find an equation for the graph sketched below.
Answers
The equation for the graph sketched below is given as y = -3(3)^x
Exponential equationThe standard form of an exponential equation is given as y = ab^x
Using the coordinate points on the graph (-1, 1) and (0, -3)
The equivalent equations are;
1 = ab^-1
-3 = ab^0
From equation2;
a= -3
Substitute into equation 1;
1 = ab^-1
1 = 3b^-1
1 =3/b
b =3
Determine the equation
y = ab^x
y = -3(3)^x
This gives the required exponential equation
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Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary.
sin θ = 0.7071 O = 5 H = ?
Answers
By applying sine trigonometry, the angle θ in this right angled triangle is approximately equal to 50 degrees.
What is the law of sines?In Trigonometry, the law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
How to apply basic trigonometry?In order to determine the value of H, we would apply basic trigonometry. From the information provided about this right angled triangle, we can logically deduce the following parameters:
sinθ = 0.7071Opposite (Opp) = 5Hypotenuse (Hyp) = H.Therefore, we would use the sine trigonometry to determine the value of H as follows:
Sinθ = Opp/Hyp
0.7071 = 5/H
H = 5/0.7071
H = 7.0711.
Now, we can determine the angle θ in this right angled triangle as follows:
Sinθ = Opp/Hyp
Angle, θ = sin⁻¹(Opp/Hyp)
Angle, θ = sin⁻¹(5/7.0711)
Angle, θ = sin⁻¹(0.7071)
Angle, θ = 44.999 ≈ 50°.
Angle, θ = 50 degrees.
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Pls help will rate 5 stars and maybe also brainliest. Pls help anyways tysm
Answers
Answer:
1. Decimal: 0.1 Fraction: 1/10
2. Decimal: 0.8 Fraction: 8/10
3. Decimal: 0.4 Fraction: 4/10
4. Decimal: 0.6 Fraction: 6/10
5. Decimal: 0.7 Fraction: 7/10
Explaination:
brainliest me if it helps!
Need help with this one
Answers
Answer: The answer should be 10^2 or C
Step-by-step explanation: 65.108 if you move the six to left 2 times you will get 6,510.8
Whats the correct answer answer asap for brainlist
Answers
Answer:
It is A how the body responds to a change
x = -CD/CD2-40 DC8x2 + 8x = -2Write the quadratic equation in standard form:( a )x2 + ( b )x+ C) = 0Identify the values of a, b, and c.b =Substitute these values into the quadratic formula and simplify:2( )a =C=
Answers
So the initial equation is:
[tex]8x^2+8x=-2[/tex]To writte the equation in the standard form we have to make it equal to 0, so we can add 2 in bout sides of the equation:
[tex]\begin{gathered} 8x^2+8x+2=-2+2 \\ 8x^2+8x+2=0 \end{gathered}[/tex]now, (a) is the number thas goes with the x^2, (b) is the number that goes with the x and (c) is the number that is alon, so:
[tex]\begin{gathered} a=8 \\ b=8 \\ c=2 \end{gathered}[/tex]Now we can substitute this numbers in the quadratic equation:
[tex]\begin{gathered} \frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \frac{-8\pm\sqrt[]{8^2-4(8)(2)}}{2(8)} \end{gathered}[/tex]and finally we can simplify the equation:
[tex]\begin{gathered} \frac{-8\pm\sqrt[]{64-64}}{16} \\ \frac{-8}{16}=\frac{-4}{8}=\frac{-2}{4}=-\frac{1}{2} \end{gathered}[/tex]solve. -6 4/9 - 3 2/9 - 8 2/9
Answers
Answer:
the answer is -17 8/9
Step-by-step explanation:
when "subtracting" negative numbers you actually add all of them together and attach the negative sign
When a number is added to 20 and 5 is subtracted from the number, their product is 150. Find the two possible numbers
Answers
Answer:
--15 and --10 respectively
Step-by-step explanation:
Let the first no be a and second no be b
From the interpretation of the question
a + 20 (added) -- 5 (subtracted) = 0
a + 20 -- 5 = 0
a + 15 = 0
a = --15
Product = 150
a×b = 150
(--15) × b = 150
b = --150/15
b = --10
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The graph below shows the relationship between population density and pollution per person for 36 Japanese cities.what is the best description of this relationship?____________________* Positive linear association* Negative linear association* Nonlinear association* No association
Answers
Answer:
No association
Explanation:
If there is a positive linear association, the graph would show something close to a straight line with a positive slope.
In the same way, if there is a negative linear association, the graph would be a straight line with a negative slope
If there is a nonlinear association we would see a curve.
Since all the data is dispersed in the graph, we can say that the best description of this relationship is No association.
Please show work THANK YOU
Answers
The net force acting on the object is 12.44 N.
In this problem, we are dealing with the magnitude of a vector, where A vector is an object that has both a magnitude and a direction. Geometrically, able to picture a vector as a directed line segment, whose length is the magnitude of the vector, and with an arrow showing the direction. A vector's magnitude is the length of the vector. The magnitude of the vector a is signified as ∥a∥. Since we are provided with magnitudes of the three forces acting on the object which are (-8,5), (0,1), and (4, -7) So we can represent them in terms of vectors which are :
F₁= -8i+5j
F₂= j
F₃ = 4i-7j
The magnitude of a vector is basically to add the individual horizontal and vertical components to get the horizontal and vertical components of the resultant force, then sum up the square of the vertical components and horizontal of the resultant force and take the square root of the result.
F(net) =[tex]\sqrt{}[/tex]( F₁²+ F₂²+ F₃²)
=[tex]\sqrt{}[/tex] ((-8)²+(0)²+(4)²) +((5)²+ (1)²+(-7)²)
=[tex]\sqrt{}[/tex](64+16)+(25+1+49)
= 12.44 N
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Which expression is equivalent to one third times the quantity 2 times x plus 12 end quantity minus 14 over 15 times x?
one and three fifths times x plus four
four fifteenths times x minus 4
negative four fifteenths times x minus four
negative 4 over fifteen times x plus four
Answers
Option Negative 4 over fifteen times x plus four is equivalent to expression one third times the quantity 2 times x plus 12 end quantity minus 14 over 15 times x.
Firstly writing the mentioned expression in mathematical form -
Expression = 1/3(2x + 12) - 14x/15
Simplifying the expression by performing multiplication
Expression = 2x/3 + 12/3 - 14x/15
Taking LCM of these three denominator, we get 15
Expression = 2x×5 + 12×5 - 14x/15
Performing multiplication in numerator of the Right Hand Side of the expression
Expression = 10x + 60 - 14x/15
Performing subtraction
Expression = - 4x + 60/15
Rewriting the expression
Expression = - 4x/15 + 60/15
Performing division on extreme Right Hand Side of the expression
Expression = - 4x/15 + 4
Thus, the correct equivalent expression is option negative 4 over fifteen times x plus four.
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Write .242424... as a
fraction in lowest terms
Answers
Answer: 8/33
Step-by-step explanation:
r = 0.242424....
100r= 24.2424....
100r - r = 99r
99r = 24
r = 24/99 = 8/33
2. Let f(x) = 5x² - 2x - 7.
(a) find f(0)
(b) find f(-3)
(c) find x if f(x) = 0
Answers
(B) Same calcul with -3 f(-3) = 25
(C) delta = b^2 - 4ac
= -2^2 - 4*5*(-7)
= 4 + 140
= 144 so delta>0 2 solutions
X1 = -10/10 = -1
X2 = 14/10 = 7/5
Answer:
A) f(0) = -7
B) f(-3) = 44
C) x = -1, (7/5)
Step-by-step explanation:
2. Let f(x) = 5x² - 2x - 7.
(a) find f(0)
f(x) = 5x² - 2x - 7
f(0) = 5(0)² - 2(0) - 7
f(0) = -7
(b) find f(-3)
f(x) = 5x² - 2x - 7
f(-3) = 5(-3)² - 2(-3) - 7
f(-3) = 5(9) - 2(-3) - 7
f(-3) = 45 + 6 - 7
f(-3) = 45 + 6 - 7
f(-3) = 44
(c) find x if f(x) = 0
f(x) = 5x² - 2x - 7
f(x) = 5x² - 2x - 7 = 0
(5x² + 5x)(-7x - 7)
5x(x + 1) -7(x + 1)
(5x - 7)(x + 1)
5x - 7 = 0, x + 1 = 0
+7 +7 -1 -1
--------------- ---------------
5x = 7 x = -1
÷5 ÷5
------------
x = (7/5)
5(-1)² - 2(-1) - 7 = 0
5(7/5)² - 2(7/5) - 7 = 0
----------------------------------------------------------------------------------------------------------
I hope this helps!
Consider the transformation shown.
6
8
Pre-image
Intro
10
3
5
Image
Use the drop-down menus to complete the sentence.
The transformation is
because the
preserved.
Done
Answers
The transformation is non rigid
What transformations ?Transformations involve the rotation, reflection, or translation of forms on a coordinate plane. Transformational geometry is a fresh viewpoint on geometry that Felix Klein suggested in the 19th century. The majority of geometric proofs rely on the transformations of objects. Any image in a coordinate plane can be changed using transformations. Applying the transformational laws will help you better understand the graphics in video games. Learn to recognize transformations, comprehend function transformation principles, and investigate the various forms of transformations.
What is non rigid transformations ?Non-Rigid Transformations actually alter the original object's structure. Scaling, for instance, allows us to make our object larger or smaller. Alternatively, shearing can be used to "push" it up or to the side. In essence, non-rigid transformations allow an object's size to change.
because the size became small as compare to pre image it is non rigid transformation
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If Thiyo traveled 420 miles at the same rate, how many hours did he drive?Enter your answer as a decimal into the box. h
Answers
Solution:
Speed is expressed as
[tex]\text{speed = }\frac{dis\tan ce\text{ covered}}{time\text{ taken}}[/tex]Given that Thiyo traveled 420 miles at 56 mi/h, let t represent the number of hour he drove.
Thus,
[tex]56\text{ mi/h = }\frac{420\text{ miles}}{t}[/tex]Make t the subject of the formula.
[tex]\begin{gathered} 56\text{ mi/h = }\frac{420\text{ miles}}{t} \\ \text{Multiply through by t} \\ t(56\text{ mi/h) = t(}\frac{420\text{ miles}}{t}) \\ 56t=420 \\ \text{divide both sides by the coefficient of t, which is 56.} \\ \text{thus, } \\ \frac{56t}{56}=\frac{420}{56} \\ \Rightarrow t=7.5\text{ hours} \end{gathered}[/tex]Hence, Thiyo drives for 7.5 hours.
Chris and Beth Micelli made a $235,000 offer for the purchase of a new home, which was accepted. They made a 30% down payment and financed the rest. Using the closing cost table below, find the mortgage total if they include the closing costs in the mortgage amount.
Answers
The amount of mortgage will be the remaining amount after they made a downpayment.
Since the downpayment is 30%, the mortgage will be 70% of the purchased amount
So mortage will be :
mortgage = 0.70 x $235,000 = $164,500
From the closing cost table :
There are charges related to the mortgage (Points, Document stamp and Processing fee)
Adding these charges will be :
=2% + 0.30% + 1.10% = 3.4% of the mortgage
So this will give us :
= 0.034 x $164,500 = $5,593
Now to find the total mortgage, add the values in the closing cost table including the mortgage itself.
Total mortgage = 164500 + 5,593 + 252 + 65 + 325 + 212 + 410 + 350 + 450
Answer :
Total mortgage = $172,157
Please help me I was sick today and missed out on class and I don’t understand this question
Answers
i.
it is an corresponding angles
ii.
the realtion we have is that the angles are equal
iii.
4+10x=11x-1
or 4+1=11x-10x
5=x
iv
4+10x=4+10×5
=54
11x-1=11×5-1=54
Answer:
A)Corresponding angles (When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles
B)They are congruent to each other
C) 4+10x=11x-1
4=x-1
5=x
( we put them equal to each other because they are the same)
D)4+10(5)=
4+50=54
D)11(5)-1=
55-1=54