Answers
By interpreting the vertex form of the equation of parabola, the focus of the curve is equal to F(x, y) = (2, 0). (Correct choice: D)
How to determine the coordinates of the focus of a parabola
In this problem we find the equation of a parabola in standard form, which has to be rearranged into its vertex form in order to determine the coordinates of its focus.
The focus of a parabola is a point outside the curve such that the least distance from any point of the parabola and the least distance between that the point on the parabola and directrix are the same.
First, rearrange the polynomial into its vertex form by algebraic handling:
y = (1 / 8) · (x² - 4 · x - 12)
y + (1 / 8) · 16 = (1 / 8) · (x² - 4 · x - 12) + (1 / 8) · 16
y + 2 = (1 / 8) · (x² - 4 · x + 4)
y + 2 = (1 / 8) · (x - 2)²
y + 2 = [1 / (4 · 2)] · (x - 2)²
Second, determine the vertex and the distance between the vertex and the focus:
The parabola has a vertex of (h, k) = (2, - 2) and vertex-to-focus distance of 2.
Third, determine the coordinates of the focus:
F(x, y) = (h, k) + (0, p)
F(x, y) = (2, - 2) + (0, 2)
F(x, y) = (2, 0)
The focus of the parabola is equal to F(x, y) = (2, 0).
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Related Questions
what does this mean 3|-3| the whole |-3| thing I'm confused please help
Answers
|-3| means "the absolute value of 3", which is a way of saying how far away from zero the number -3 is on the number line.
The definition of absolute value goes like this:
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
In other words, if the number [tex]x[/tex] inside the absolute value bars is already positive or zero, we leave it alone. If instead [tex]x[/tex] is negative, we multiply it by -1 to recover the positive version of that number.
Since -3 is negative, it follows that |-3| = -(-3) = 3. So the expression 3 |-3| is equivalent to 3 • 3 = 3² = 9.
please answer preferably with steps, but not necessary
Answers
Answer:
Step-by-step explanation:
(5n - 3)/2=n-0.3
Then we solve for n.
Multiply the whole thing by 2.
5n-3=2n-0.6
Add 0.6
5n-2.4=2n
Add 2.4
5n=2n+2.4
Subtract 2n
3n=2.4
Divide by 3
n=0.8
Jason made a spherical cake pop that is 1.3 inches in diameter. He coated the whole cake pop with sprinkles.What is the approximate area Jason covered with sprinkles?
Answers
Given:
The diameter of the sphere is 1.3 inches.
The surface area of the sphere is given as,
[tex]\begin{gathered} SA=4\pi\times r^2 \\ SA=4\pi\times(\frac{d}{2})^2 \\ SA=4\pi\times(\frac{1.3}{2})^2 \\ SA=1.69\pi \\ SA=1.69\times3.14\ldots\ldots\pi=3.14 \\ SA=5.3066 \\ SA\approx5.3\text{ square inches} \end{gathered}[/tex]Answer: area covered with sprinkles is 5.3 square inches
Describe and correct the error in evaluating the expression.
9 + 2 x 3 = 11 x 3 = 33
How would you write this problem with the multiplication first?
Answers
The error in the solution is adding 9 and 2 before the multiplication and the new expression is (2 x 3) + 9
The description of the error?The equation and the steps are given as
9 + 2 x 3 = 11 x 3 = 33
The above solution is incorrect
This is so because the product has a higher order of precedence
So, it must be evaluated first
So, the correct solution is
9 + 2 x 3 = 9 + 6 = 15
To rewrite the expression such that the product is done first, we introduce the use of brackets
So, we have
9 + (2 x 3)
This gives
(2 x 3) + 9
Hence, the result of the products is (2 x 3) + 9
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Can someone please help me with this geometry question
Answers
Write .24 as a fraction
in lowest terms.
Answers
Answer:
.24 as a fraction is 6/25
Step-by-step explanation:
1) Let convert our decimal into a percentage so we could write it in the not simplified fraction of 0.24:
.24 = 24% = 24/100
2) Now since we have 24/100, we could now simplify:
24/100 = 12/50 = 6/25
We can't simplify anymore.
Answer: 6/25
Step-by-step explanation:
Find the y intercept (if there is one) put your answer as a ordered pair.
(-2,6) (1,6)
Answers
The y-intercept of the line that passes through points (-2,6) and (1,6) in an ordered pair is ( 0,6 ).
What is the y-intercept of the line that passes through the given points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
The slope of a line is expressed as change in y over change in x.
Slope m = (y₂-y₁)/(x₂-x₁)
Given the data in the question;
Point A ( -2,6 )
x₁ = -2y₁ = 6Point B ( 1, 6 )
x₂ = 1y₂ = 6First, we determine the slope of the line.
Slope m = (y₂-y₁)/(x₂-x₁)
Slope m = ( 6 - 6 )/( 1 - ( -2) )
Slope m = ( 0 )/( 1 + 2) )
Slope m = ( 0 )/3
Slope m = 0
Now, we can determine the y-intercept b, using the slope and coordinates of 1 point.
y = mx + b
6 = (0)(1) + b
Solve for b
6 = 0 + b
b = 6
Therefore, the coordinates of the y-intercept is ( 0,6 ).
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25×10 to the power of -3 to standard form
Answers
The number 25×10 to the power of -3 written in the standard form is 2.5×10⁻⁴.
What is meant by the term scientific notations?Scientific notation is a way of displaying very large or extremely small numbers in a more simplified format. We know that whole numbers could be extended indefinitely, but such large numbers cannot be written on a sheet of paper. The scientific notation allows us to represent very large or very small numbers by multiplying single-digit numbers by 10 raised to a power of a respective exponent. If the number is so very large, the exponent is positive; otherwise, it is negative. For a better understanding, learn power and exponents.The given number is;
25×10 to the power of -3
This can be written as;
= 25×10⁻³
Now, as per the standard form, the number should contain only one digit to the left of decimal.
Thus, shifting one decimal to the left of the 5 and converting the power by adding one to the current power,.
The number becomes;
= 2.5×10⁻⁴.
Thus, the number written in the standard form is 2.5×10⁻⁴.
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A spinner with 10 equally sized slices has 5 red slices , and 3 yellow slices, and 2 blue slices. The dial 500 times and got the following results. What is the probability that the dial stops on a red or yellow slice?
Answers
Part a
The experimental probability that landing on red is equal to
P=277/500
P=0.554
Part b
The theoretical probability that landing on red is equal to
P=5/10
P=0.5
Part c
the answer is the first option
Which expression does not belong with the other three? justify your response.
Answers
To find the equation that does not belong with the other three we have to solve each equation.
Given the equation:
[tex]4\cdot x\cdot7=56[/tex]Dividing by 4 at both sides:
[tex]\begin{gathered} \frac{4\cdot x\cdot7}{4}=\frac{56}{4} \\ x\cdot7=14 \end{gathered}[/tex]7:
[tex]\begin{gathered} \frac{x\cdot7}{7}=\frac{14}{7} \\ x=2 \end{gathered}[/tex][tex]5\cdot2\cdot x=40[/tex]Simplifying on the left:
[tex]10\cdot x=40[/tex]10:
[tex]\begin{gathered} \frac{10\cdot x}{10}=\frac{40}{10} \\ x=4 \end{gathered}[/tex]:
[tex]x\cdot3\cdot9=54[/tex][tex]x\cdot27=54[/tex]27:
[tex]\begin{gathered} \frac{x\cdot27}{27}=\frac{54}{27} \\ x=2 \end{gathered}[/tex][tex]4\cdot x\cdot5=40[/tex]4 :
[tex]\begin{gathered} \frac{4\cdot x\cdot5}{4}=\frac{40}{4} \\ x\cdot5=10 \end{gathered}[/tex]5
[tex]\begin{gathered} \frac{x\cdot5}{5}=\frac{10}{5} \\ x=2 \end{gathered}[/tex]In consequence, the equation that does not belong with the other three is:
[tex]5\cdot2\cdot x=40[/tex]because its solution, 4, is different from the solution to the other equations (2).
If we change the 5 in the equation by a 10 and solve the equation we get:
[tex]\begin{gathered} 10\cdot2\cdot x=40 \\ \frac{10\cdot2\cdot x}{10}=\frac{40}{10} \\ 2\cdot x=4 \\ \frac{2\cdot x}{2}=\frac{4}{2} \\ x=2 \end{gathered}[/tex]And now the equation (with a 10) belongs with the other three
28•x=56 1)x=2
10•x=40 2)x=4
27•x=54. 3)x=2
20•x=40. 4)x=2
good luck!
how do I solve this
1/9 = z/23
Answers
Answer: z=23/9
Step-by-step explanation:
I will use cross multiplication
[tex]\frac{1}{9} =\frac{z}{23} \\23(1)=9(z)\\23=9z\\\frac{23}{9} =\frac{9z}{9} \\z=\frac{23}{9}[/tex]
I hope this helps.
Select the correct equation and correct answer to solve for X using the triangle below.
Answers
The correct equation to solve for x is 2(2x-15)=2x-8 , and the value of x is 11 .
in the question ,
from the given figure , we can see that RL=LQ and PK=KQ which means
that L and K are the mid points of sides RQ and PQ respectively .
The Mid Point Theorem states that
If the line segment adjoining the mid points of any of the sides of the triangle then the line segment is said to be parallel to the third side and is half of the length of third side .
which means LK parallel to RP and RP/2=LK ( ... by mid point theorem)
Substituting the values of LK = 2x-15 and RP = 2x-8 .
(2x-8)/2=2x-15
Multiplying both sides by 2
2x-8 = 2(2x-15)
So, the equation to solve for x is 2(2x-15)=2x-8
Simplifying further
2x-8 = 4x-30
4x-2x= 30-8
2x = 22
x = 11
Therefore , the correct equation to solve for x is 2(2x-15)=2x-8 , and the value of x is 11 .
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Slope intercept form for points through (0,4) and (-3,3)
Answers
Answer:
y = (1/3)x + 4
Step-by-step explanation:
(0, 4) and (-3, 3)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 3 - 4 -1 1
m = ------------- = ------------ = --------- = --------
x₂ - x₁ -3 - 0 -3 3
y - y₁ = m(x - x₁)
y - 4 = (1/3)(x - 0)
y - 4 = (1/3)x - 0
+4 +4
----------------------------
y = (1/3)x + 4
I hope this helps!
what picture can you draw to show a thinking about 9÷4?
Answers
Think of
[tex]\frac{Green}{Red}[/tex]15. Over what range of angles does the value of sin(O) consistently increase?
A. 45° to 135°
B. 90° to 180°
C. 0° to 180°
D. 0° to 90°
Answers
The value of sin(O) will at the range of 0° to 90° consistently increase. This makes option D the correct options.
how to find the range of values where sin will consistently increaseIn trigonometry, the first basic functions are the sin, cos and tan.
In a right angle triangle the sin is represented as the ratio of opposite to hypotenuse. cos is represented as the ratio of the adjacent to hypotenuse, while tan is the ratio of opposite to adjacent or ratio of sin to cos.
Plotting the graph of sin functions, the pattern forms a sinusoidal pattern which bears its maximum value at sin 90degrees and the minimum value at sin 0 degrees.
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Two numbers are respectively 60% and 20% of a third number, second number exepress ss as a perentage of first is?
Answers
Answer:
10%
Step-by-step explanation:
this is because the total number is supposed to be 100%
and 60%+20%=90%. 100%-90%=10%.
So 10% is the final answer
A constant force is applied to an object, causing the object to accelerate at 12.50 m/s/s. What will the acceleration be if both the force and the
mass are doubled? Round to two decimal places and use SI units.
Answers
Answer:
a₂ = 12.5 m/s²
Step-by-step explanation:
Applying the 2º Newton's Law:
∑F = m * a
F₁ = m₁ * a₁
F₁ = m₁ * 12.5
F₁ = 12.5m₁
F₂ = m₂ * a₂
2F₁ = 2m₁ * a₂
a₂ = F₁ / m₁
So:
a₂ = 12.5m₁ / m₁
a₂ = 12.5 m/s²
BenchenIf these two lines were graphed, where would they intersect? Drag the point to theirintersection's coordinates.y = x - 3y = -X- 1
Answers
y = x - 3
y = - x -1
They intersect at
Find the x-intercept of the line that passes through (-3,4) and is perpendicular to the graph of x-2y=7
Answers
Answer:
x - intercept = - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x - 2y = 7 ( subtract x from both sides )
- 2y = - x + 7 ( divide through by - 2 )
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{7}{2}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then
y = - 2x + c ← is the partial equation of the perpendicular line\to find c substitute (- 3, 4 ) into the partial equation
4 = 6 + c ⇒ c = 4 - 6 = - 2
y = - 2x - 2 ← equation of perpendicular line
to find the x- intercept let y = 0 into the equation and solve for x
- 2x - 2 = 0 ( add 2 to both sides )
- 2x = 2 ( divide both sides by - 2 )
x = - 1
the x- intercept of the perpendicular line is - 1 or (- 1, 0 )
HELP ME PLEASE SOON NEED RN
Answers
Answer:
x = + or - 8
Step-by-step explanation:
2x^2 = 128
solve for x
hope this helped have a great day ^^
please help im begging ill give brainliest
Answers
Answer:
t=44 hrs.
Step-by-step explanation:
1. a. you are asked to find the total hours the 2 girls work in a week.
b. it needs to be a greater number than 26
2. variables: h= hours per week
t= total hrs.
3. h= hrs. per week
t= total hrs.
4. 44=26+h
-26 -26
18=h
5. 44=26+18
44=44
6. The total hours the two work in a week is 44 hours.
Describe the transformation that maps the pre-image A to the image A.translated 8 units up and then reflected across the y-axisB)translated 8 units down and then reflected across the y-axisC)translated 1 unit to left and then rotated 180° counterclockwise about theoriginD)translated 1 unit to right and then rotated 180° counterclockwise about theorigin
Answers
Answer:
C. translated 1 unit to left and then rotated 180° counterclockwise about the
origin
Explanation:
In the graph:
• The vertices of Figure A are: (0,4), (-9,3) and (-9,6)
,• The vertices of Figure A' are: (1,-4), (10,-3) and (10,-6)
If Figure A is translated 1 unit to the left, the vertices are:
[tex](-1,4),(-10,3),(-10,6)[/tex]Next, a rotation of 180° counterclockwise about the origin gives:
[tex](1,-4),(10,-3),(10,-6)[/tex]These are the vertices of Figure A'.
Thus, the correct transformation is: translated 1 unit to left and then rotated 180° counterclockwise about the origin.
The correct choice is C.
Help me answer this.
Answers
iven:
here are givren the expression:
[tex](2z-y)^{20}[/tex]xplanation:
o find the coefficient of the given expression, we need to use the binomial expansion formula:
So,
From the formula of binomial expansion:
[tex](x+y)^n=\sum_{k\mathop{=}0}^n(n,k)x^ky^{n-k}[/tex]then,
After using the above formula in the given binomial, the expansion will be:
[tex](2z-y)^{20}=y^{20}-40y^{19}z+760y^{18}z^2-9120y^{17}z^3+77520y^{16}z^4-496128y^{15}z^5+...[/tex]inal answer:
ence , the coefficient of the given term is shown below:
[tex]77520[/tex]A passenger car will go 310 miles on 15.5 gallons of gasoline in city driving. What is the rate in miles per gallon?
The rate is
mpg.
(Simplify your answer.)
Answers
Answer:
20 mpg
Step-by-step explanation:
Given:
A passenger car will go 310 miles on 15.5 gallons of gasoline in city driving. What is the rate in miles per gallon?
Solve:
To find the rate in miles per gallon we have to divide.
Knowing that "Per" means "Each/One"
Hence, to find miles per gallon we divide :
Miles by Gallons
⇒ 310/15.5
Solving using long division format: ( Multiply both by 10 first)
[tex]155\overline{|\smallspace3100}\:\:\:\:[/tex]
Divide 310 by 155 to get 2:
[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace2\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 155\overline{|\smallspace3100}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace3\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
Divide 0 by 15.5 to get 0.
[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace2\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ 155\overline{|\smallspace3100}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace3\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
Hence, the rate is 20 mpg.
~kavinsky
Can someone help me with this please and thank you!
Answers
Answer: b
Step-by-step explanation:
The area of a circle is 100π cm². What is the circumference, in centimeters? Express your answer in terms of \piπ. THE ACTUAL ANSWER PLEASE
Answers
Answer:
35.45
Step-by-step explanation:
C=2πA=2·π·100≈35.44908
Kendall read 1 1/3 books in a 1/2day. At that rate how many books will she read in
1 day?
Answers
Answer:
Step-by-step explanation:
1/2 to 1 day is 2 1/2
11/3 x 11/3 = 121/9
13.4 books
Help
Simplify the negative exponent. Please show your work.
4 ⁻⁴
Answers
Answer: 0.0625
Step-by-Step Explanation: positive exponents = multiply the number by itself however many times the exponent demands.
negative exponents: multiply the reciprocal of the base number by itself however many times the exponent demands.
STEP-BY-STEP EXPLAINED
the lewis family drove 45.6 miles to the river. It took them 1.2 hours to get there. How fast did they drive? Round to the nearest whole number
Answers
The most appropriate choice for speed will be given by
Speed of the car of Lewis family = 38 miles/hours
What is speed?
Distance travelled by an object per unit of time is called speed.
If d is the distance travelled and t is the time taken, then speed is calculated by-
Speed = [tex]\frac{d}{t}[/tex]
Here, speed is a scalar as the direction is not taken into account.
Distance drove by Lewis family to the river = 45.6 miles
Time taken by the Lewis family to go to the river = 1.2 hours
Speed of the car of Lewis family = [tex]\frac{45.6}{1.2}[/tex]
= 38 miles/hour
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A large group is ordering shirts for a company outing. The order will be based on how many employees sign up for a shirt.
The independent variable in this situation is the size of the order.
True
OR
False
Answers
Answer:
False
Step-by-step explanation:
The dependent variable changes, the size of the order will change depending on how many employes want a shirt.