Answer:
[tex]y=-1[/tex]
Step-by-step explanation:
We have been given an equation of parabola [tex]x^2=4y[/tex]. We are asked to find the directrix of our given parabola.
First of all, we will divide both sides of our given equation by 4.
[tex]\frac{x^2}{4}=\frac{4y}{4}[/tex]
[tex]\frac{x^2}{4}=y[/tex]
[tex]y=\frac{x^2}{4}[/tex]
Now, we will compare our equation with vertex form of parabola:
[tex]y=a(x-h)^2+k[/tex], where, (h,k) represents vertex of parabola.
We can see that the value of a is [tex]\frac{1}{4}[/tex], [tex]h=0[/tex] and [tex]k=0[/tex].
Now, we will find distance of focus from vertex of parabola using formula [tex]p=\frac{1}{4a}[/tex].
Substituting the value of a in above formula, we will get:
[tex]p=\frac{1}{4*\frac{1}{4}}[/tex]
[tex]p=\frac{1}{1}=1[/tex]
We know that directrix of parabola is [tex]y=k-p[/tex].
Substituting the value of k and p in above formula, we will get:
[tex]y=0-1[/tex]
[tex]y=-1[/tex]
Therefore, the directrix of our given parabola is [tex]y=-1[/tex].
PLEASE HELP! BRAINIEST GETS 50 POINTS!
14. The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 4 + 2x. What does the y-intercept of this function represent?
A) The original height of the plant was 4 mm.
B) The original height of the plant was 2 mm.
C) The height of the plant increases by 2 mm for every hour of sunlight it receives.
D) The height of the plant increases by 4 mm for every hour of sunlight it receives.
16. The table below shows the values of y for different values of x:
x 7 8 9 10 11 12 13
y 3 5 7 9 10 13 14
The correlation coefficient for the data is 0.9976. Which statement is true about the data in the table?
A) There is a strong positive relationship between x and y.
B) There is a strong negative relationship between x and y.
C) There is a weak positive relationship between x and y.
D) There is a weak negative relationship between x and y.
10. Two groups of students were asked how far they lived from their school. The table below shows the distances in miles:
Group A (distance in miles) 1 1.5 3 3.2 2.8 1.5 1.8 2.5 2.2
Group B (distance in miles) 2 2.5 3.2 3 1.8 2.4 3 1.5 1.8
Which statement best compares the mean distances for the two groups?
A) It is equal for Group A and Group B.
B) It is greater for Group B than Group A.
C) Its value for Group A is double its value for Group B.
D) Its value for Group B is double its value for Group A
DONT ANSWER IF YOU'RE NOT 100% CERTAIN...I NEED TO PASS
Answer:
Ok so the first one, your answer will be C. The height of the plant increases by 2 mm for every hour of sunlight it receives. For the second one, It is B.There is a strong negative relationship between x and y. And the last one is B. It is greater for Group B than Group A.
Step-by-step explanation: Hopes this helps!!! :)
HURRY, PLEASE I NEED HELP!!!
the measures of the angle of,triangle, ABC are given by the expressions in the table.
angle measure
A (4x-13)
B 15
C (x+18)
what is the measure of A and C
enter your answers in the boxes
m A=___
m C=___
In a triangle we apply angle sum property of triangle, which is given by:
Sum of angles of triangle =180 degrees.
We are given three angles,
A =(4x-13)
B =15
C =(x+18)
Adding the three angles and equating it to 180,
[tex] (4x-13) +15 + (x+18) =180 [/tex]
combining like terms
[tex] 5x+20 =180 [/tex]
[tex] 5x=180-20 [/tex]
[tex] 5x =160 [/tex]
x=32
angle A = 4x-13 = 4(32)-13 = 115 degrees.
angle C = x+18 = 32 +18 = 50 degrees.
Answer : angle A is 115 degrees and Angle C is 50 degrees.
Analyze the diagram to complete the statements. The m∠MXN is the m∠YZX. The m∠LZX is the m∠ZYX + m∠YXZ. The m∠MYL is 180° − m∠ZYX.
By using the picture that was provided below, you can see that
m<MXN is greater than m<YZX.
Angles m<LZX is equal to m<ZYX + m<YZX and
m<MYL is equal to 180 degrees minus M<ZYX.
I hope this helps! Have a good day
Answer:
Step-by-step explanation:
What is the approximate value of the function at x = 0?
a) -3
b) -4
c) -5
d) -4.5
Six friends each put $250 into a single account that earns 5.5% annually. The interest earned is added to the account at the end of each year. The friends want to use the money in the account to go on a vacation after four years. The friends get together after most have finished college four years later. How much money is in the account?
In the figure, TU is tangent to the circle at point U. Use the figure to answer the questions.
(a) Describe the relationship among the lengths of the segments formed by the secant, RT, and the tangent segment, TU. You may use words and/or an equation.
(b) Suppose RT = 9 in. and ST = 4 in. Is it possible to find the length of TU? If so, show how to find the length. If not, explain why not.
Both the parts of this question require the use of the "Intersecting Secant-Tangent Theorem".
Part A
The definition of the Intersecting Secant-Tangent Theorem is:
"If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment."
This, when applied to our case becomes, "The length of the secant RT, times its external segment, ST, equals the square of the tangent segment TU".
Mathematically, it can be written as:
[tex] RT\times ST=(TU)^2 [/tex]
Part B
It is given that RT = 9 in. and ST = 4 in. Thus, it is definitely possible to find the value of the length TU and it can be found using the Intersecting Secant-Tangent Theorem as:
[tex] RT\times ST=(TU)^2 [/tex]
Thus, [tex] (TU)^2=9\times 4=36 [/tex]
[tex] \therefore TU=\sqrt{36}=6 [/tex]
Thus the length of TU=6 inches
Class 10R sat a test. The mean mark of the class was 70%. There are 30 students in class 10R, 20 of whom are boys. The mean mark for the boys in the test was 62%.Work out the mean mark for the girls.
86%
70X30=2100
20X62=1240
2100-1240 = 860
860/10=86
Answer:
Mean mark for the girls is [tex]86%[/tex].
Step-by-step explanation:
Given information:
Number of total students in the class=[tex]30[/tex]
Number of boys in the class=[tex]20[/tex]
Then, number of girls will be=[tex]30-20[/tex]=[tex]10[/tex]
The mean mark of the class=[tex]70\times30=2100[/tex]
The mean mark for the boys is [tex]62[/tex]
Then, mark for the boys[tex]=62\times20=1240[/tex]
The mark for the girls=[tex]2100-1240=860[/tex]
Then mean mark of the girls will be [tex]\frac{860}{10}=86[/tex]
Hence, mean mark for the girls is [tex]86%[/tex].
For more details please refer link :
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Wendy enjoys listening to hip hop and downloads music regularly from the internet. She already has four hours of hip hop in her collection. From the second month onward, the number of hours of hip hop music she downloads each month is nine percent greater than the number of hours of hip hop music she had downloaded the previous month. Which function best shows the total number of hours of hip hop music Wendy has in her collection f(x) after x months? f(x) = (1.09)x + 3 f(x) = 3(1.09)x f(x) = (1.09)x + 2 f(x) = (1.09)x - 2
the sum of 5 consecutive odd number is 145
Which equation represents a line which is parallel to the line x-8y=48 x−8y=48?
The required line is y = x/8 - 6 which is parallel to the given line x − 8y = 48.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The slope-intercept form is y = mx+c, where the slope is m and the y-intercept is c
The equation is given in the question below as
x − 8y = 48
We have to convert the equation to slope-intercept form
x − 8y = 48
− 8y = - x + 48
Divided by -8 into both sides of the above equation,
− 8y / (− 8) = - x / (− 8) + 48 / (− 8)
y = x/8 - 6
Since the slope is the same, therefore the lines are parallel.
Therefore, the required line is y = x/8 - 6 which is parallel to the given line x − 8y = 48.
Hence, the correct answer would be an option (A).
Learn more about the Linear equations here:
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The question seems to be incomplete the correct question would be
Which equation represents a line which is parallel to the line x − 8y = 48?
A. y = x/8 - 6
B. y = x/2 - 8
C. y = x/6 - 4
D. y = x/4 - 2
what is the value of x if the equation is
x+90+18.4
What is this answer?
Miguel had 63 lemons to make lemonade at his stand. He used some lemons to make lemonade. Now he has 25 lemons. How many lemons did Miguel use?
Miguel used ___lemons to make lemonade.
Answer: He used 38 lemonsssssssssssss
Step-by-step explanation:
An object is traveling around a circle with a radius of 10 cm. If in 20 seconds a central angle of 1/3 radian is swept out, what is the linear speed of the object?
I think I've set my formula up right (v=Δ20/Δ1/3 radian), but I don't know what to do with the Δ thing. Once I know how to do that I should be able to like, actually figure it out.
simplify the expression by combining like terms. 6x - 7 + 2x + x + 2
9x - 5
8x -5
8x + 5
7x -5
Solve the equation. b + 8 = 16
B = 24
B = -24
B = 8
B = -8
Solve the equation. 6p =-84
P = -14
P = 7
P =-7
P = 14
Name the property shown. 7 + 6 = 6 + 7
Solve the equation. 15 = 5x
X = 3
X = 10
X = 14
X = 5
Consider the two triangles shown.
The second step in the process for factoring the trinomial x^2-3x-40 is to
Answer:
Second step x( x +5 ) -8 (x+ 5 ) in process of factoring .
Step-by-step explanation:
Given : Trinomial x²-3x-40 .
To find : The second step in the process for factoring .
Solution : We have x²-3x-40 .
On factoring x²+ 5x - 8x - 40 .
Taking common x from first two terms and -8 from last two terms.
x( x +5 ) -8 (x+ 5 ) .
Therefore , Second step x( x +5 ) -8 (x+ 5 ) in process of factoring .
viola makes gift baskets for valentine's day.she has 13 basket left over from last year, and she plans to make 12 more each day. if there are 15 work days unitl the day she begins to sell the baskets, how many baskets will she have to sell?
193 baskets
156 baskets
205 baskets
181 baskets
Please help thank you.
Johanna’s parents give her $10 per week for lunch money. She cannot decide whether she wants to buy or pack her lunch. If a hot lunch at school cost $2, write and solve an inequality to finding the maximum number of times per week Johanna can buy her lunch
The graphs below have the same shape. What is the equation of the blue
Answer: The correct option is B.
Explanation:
From the given figure it is noticed that the parent function is,
[tex]f(x)=x^2[/tex]
The graph of f(x) shifts 5 units right.
The transformation is defined as,
[tex]g(x)=f(x+a)+b[/tex]
Where, a shows the horizontal shifts and b shows the vertical shift.
If a<0 then the graph of f(x) shifts right side by a units and if a>0 then the graph of f(x) shifts left side by a units.
If b<0 then the graph of f(x) shifts downward by b units and if b>0 then the graph of f(x) shifts upward by b units.
Since the graph of parent function is shifts only right side by 5 units, therefore
[tex]g(x)=f(x-5)+0[/tex]
Since [tex]f(x)=x^2[/tex]
[tex]g(x)=(x+5)^2[/tex]
Thus, the correct option is B.
The function in option A represents the left shift of f(x) by 5 units. The option C represents the downward shift of f(x) by 5 units. The option D represents the upward shift of f(x) by 5 units.
Let f(x)=25x2−2 .
The function g(x) is a vertical stretch of f(x) by a factor of 2.
What is the equation of g(x)?
Enter your answer in the box.
g(x) =
We are given function f(x) = 25x^2 -2.
g(x) is a vertical stretch of f(x) by a factor of 2.
We know, the transformation rule
y= k f(x), vertical stretch by a factor k. For k>0.
Because function f(x) is being vertical stretched by a factor of 2. So, we need to multiply f(x) function by 2.
Therefore, g(x) = 2 f(x) = 2*(25x^2-2).
Therefore, g(x) = 2*(25x^2-2) or g(x) = 50x^2-4.
Answer:
The Given function is
f(x)= 25 x² -2
Now, a function g(x) is obtained when the function f(x) is stretched by a factor of 2.
Consider point (x,y) on f(x).When function is stretched vertically by a factor of 2 ,it means, the coordinate changes from (x,y) to (x,2 y).
Since we have to stretch the function as whole, we will multiply original function by 2.
So, g(x)= 2× [25 x² - 2] =50 x² -4
g(x)=50 x²- 4
A certain species of tree grows an average of 3.1 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 600 centimeters tall.
find the volume of the cylinder with the given measurement. r= 2, h= 3
Rectangle M was dilated to form rectangle M’. What ratio is the scale factor?
1/2
2/3
4/3
3/2
Solution:
we are given that
Rectangle M was dilated to form rectangle M’.
we have been asked to find
What ratio is the scale factor?
we can find the required ratio by dividing the corresponding sides of the given rectangles as below:
[tex] Ratio=\frac{6}{4}=\frac{2}{4/3}\\
\\
[/tex]
[tex] Ratio=\frac{3}{2}=\frac{6}{4} \\
\\
\
Ratio=\frac{3}{2}=\frac{3}{2}\\ [/tex]
Hence the required ratio is 3/2.
Answer:(d or 3/2
Step-by-step explanation: I took the test
3 out of every 5 picks are orange. If 12 picks are orange, how many picks are there in all?
A check is _____.
A.) Just like debit card
B.) A promissory note (I.O.U)
C.) Required to be paid by your bank when presented
D.) Not able to be forged
Answer:
B
Step-by-step explanation:
A check is an I.O.U. or a promissory note.
Leyla drops a penny from a height of 150m. How long will it take to hit the ground? Round to the nearest tenth of a second. use the formula h(t)=-4.9t²+v₀t+h₀, where v₀ is the initial velocity and h₀ is the initial height.
It will take approximately 5.5 seconds for the penny to hit the ground.
To determine the time it takes for the penny to hit the ground, we can use the given formula for the height as a function of time:
[tex]\[ h(t) = -4.9t^2 + v_0t + h_0 \][/tex]
Given that the penny is dropped and not thrown, the initial velocity [tex]\( v_0 \)[/tex] is 0. The initial height [tex]\( h_0 \)[/tex] is 150 meters. We want to find the time [tex]\( t \)[/tex] when the height [tex]\( h(t) \)[/tex] is 0, which is when the penny hits the ground.
Plugging in the known values, we get:
[tex]\[ 0 = -4.9t^2 + 0 \cdot t + 150 \][/tex] Simplifying, we have:
[tex]\[ 4.9t^2 = 150 \][/tex]
Now, we solve for [tex]\( t \)[/tex]:
[tex]\[ t^2 = \frac{150}{4.9} \][/tex]
[tex]\[ t^2 \approx 30.612244898 \][/tex]
Taking the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\[ t \approx \sqrt{30.612244898} \][/tex]
[tex]\[ t \approx 5.532851414 \][/tex]
Rounding to the nearest tenth of a second, we get:
[tex]\[ t \approx 5.5 \][/tex]
A rectangular prism has a length of 2 1/2 centimeters, a width of 2 1/2 centimeters, and a height of 5 centimeters. Justin has a storage container for the prism that has a volume of 35 cubic centimeters. What is the difference between the volume of the prism and the volume of the storage container?
Answer:
3.75
Step-by-step explanation:
Help please what is the sum?