Given:
The focus of the parabola is at (6,-4).
Directrix at y=-7.
To find:
The equation of the parabola.
Solution:
The general equation of a parabola is:
[tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex] ...(i)
Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.
The focus of the parabola is at (6,-4).
[tex](h,k+p)=(6,-4)[/tex]
On comparing both sides, we get
[tex]h=6[/tex]
[tex]k+p=-4[/tex] ...(ii)
Directrix at y=-7. So,
[tex]k-p=-7[/tex] ...(iii)
Adding (ii) and (iii), we get
[tex]2k=-11[/tex]
[tex]k=\dfrac{-11}{2}[/tex]
[tex]k=-5.5[/tex]
Putting [tex]k=-5.5[/tex] in (ii), we get
[tex]-5.5+p=-4[/tex]
[tex]p=-4+5.5[/tex]
[tex]p=1.5[/tex]
Putting [tex]h=6, k=-5.5,p=1.5[/tex] in (i), we get
[tex]y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)[/tex]
[tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex]
Therefore, the equation of the parabola is [tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex].
In an experiment on the effects of caffeine on the alertness of college students, student volunteers are randomly assigned to two groups. One group is given caffeinated coffee while the other group is given decaffeinated coffee. All participants then play a video game to assess their mental acuity, measured as their final score on the video game. In this study, the group that is given caffeinated coffee is called the:
Answer:
Experimental group
Step-by-step explanation:
During the process of a research study whereby the participants or subject are divided into groups such that some are exposed to the independent variable or treatment while the other subjects are used as control for the study, The group of participants which are exposed or given the actual treatment or independent procedure are called the experimental group. In the scenario above, experimental group are the group of students which were given caffeinated coffee which is the independent variable in this case.
I need help solving these two questions
For question 4 it also isn't D
For question 7 it also isn't B
Answer: i could be A and the next one is c
Step-by-step explanation:
Answer:
First question 8
Second question 10
Step-by-step explanation:
First question
The general formula for both secants is the entire length * the external segment.
Using an example, it is 3*(13 + 3) = 3*16
The other secant will be 4*(x + 4)
These two are equal
4(x + 4) = 3 * 16
4(x + 4) = 48 Divide by 4
x + 4 = 12 Subtract 4 from both sides
x = 8
Second Question
8(x + 8) = 6(6 + 18)
8x + 64 = 6(24)
8x + 64 = 144 Subtract 64
8x = 80 Divide by 8
x = 80 /8
x = 10
Composition of Transformations - Item 4829
The red figure is the transformed image of the blue figure.
Tanya correctly identifies a sequence of two transformations that can move the blue
figure onto the red figure.
Kurt correctly identifies a single transformation that can be used.
Use the drop-down menus below to complete the statements describing the
transformations they used.
Answer:
Tanya is reflect y axis and then 90 degrees.
Kurt is reflect over y=x
Have an amazing day! Hope This Helps :)
Joe worked for three days. On the first day, he completed 1/2 of his work. On the second day, he completed 1/3 of the remaining work. What fraction of the work was left for the third day?
Answer:
1/3
Step-by-step explanation:
first day work=1/2
work left=1-1/2=1/2
second day finished=1/3 ×1/2=1/6
work left =1/2-1/6=3/6-1/6=2/6=1/3
Doubling both the area of the bases and the height of a prism doubles its volume. T/F
Answer:
True.
Step-by-step explanation:
Answer: False
==========================================================
Explanation:
Let's consider a prism that has dimensions of
L = 3 ft W = 4 ft H = 5 ftand we'll say that the base is a rectangle with length L and width W. The area of the base is L*W = 3*4 = 12 sq ft. The volume of this prism is L*W*H = 3*4*5 = 60 ft^3
If we double the area of the base, then we go from 12 ft^2 to 24 ft^2. If we double the height, then we go from 5 ft to 10 ft.
The new volume of this larger prism is (area of base)*(height) = (24)*(10) = 240 ft^3
The jump from 60 ft^3 to 240 ft^3 is not "times 2". Instead, the multiplier is 240/60 = 4. This example shows that the volume has been quadrupled.
R. White and Co. Has total profit of 6/7 million dollars. The spinning department gave a profit 1/4 of million dollars. Find the fraction of profit from other departments.
Answer:
Fraction of profit from other departments = 17/28
Step-by-step explanation:
Total profit of R. White and Co = 6/7 million dollars
Profit from the spinning department = 1/4 of million dollars
Fraction of profit from other departments = Total profit of R. White and Co - Profit from the spinning department
= 6/7 million dollars - 1/4 of million dollars
= 6/7 - 1/4
Lowest common multiple (LCM) of 7 and 4 is 28
= (24-7) / 28
= 17/28
Fraction of profit from other departments = 17/28
Geometry, please answer question ASAP
Answer:
option d is the answer if we make this kite such that two triangles form and the use sum of interior angle property then we get the value of x and then multiple it with two
(a) An angle measures 40°. What is the measure of its complement?
(b) An angle measures 63°. What is the measure of its supplement?
Answer:
see below
Step-by-step explanation:
Complements add to 90 degrees
x+40 = 90
x = 90-40
x = 50
Supplements add to 180
y+63 =180
y = 180-63
y = 117
If the sum of the measures of two angles is 90° they are known as complementary angles.
Let the value of unknown angle be x.According to the question
⇨x + 40° = 90°
⇨x = 90° - 40° [Subtract]
⇨x = 50°
Complement angle is 50°
____________________(b)If the sum of the measures of two angles is 180° they are known as supplementary angles.
Let the value of unknown angle be x.According to the question
⇛x + 63° = 180°
⇛x = 180° - 63° [Subtract]
⇛x = 117°
Supplement angle is 117°
If the sum of the measures of two angles is 90° they are known as complementary angles.
Let the value of unknown angle be x.According to the question
⇛x + 40° = 90°
⇛x = 90° - 40° [Subtract]
⇛x = 50°
Complement angle is 50°
____________________(b)If the sum of the measures of two angles is 180° they are known as supplementary angles.
Let the value of unknown angle be x.According to the question
⇨x + 63° = 180°
⇨x = 180° - 63° [Subtract]
⇨x = 117°
Supplement angle is 117°
This diagram shows lines PQ, RS, and TV. How
many angles appear to be obtuse? Name them.
Answer:
Obtuse angles measure between 90° and 180°.
In the diagram we have:
∠PMS, ∠RMN, ∠MNV, ∠TNQObtuse angles measure less than 180° but more than right angle
Here they are
<RMN<SMP<VNM<QNTcalculate the area of a sector with radius 13m and angle 93
Answer:
137.16
Step-by-step explanation:
we have a formular of the area of a sector:
S= pi*(its angle)/360*R^2
so apply to it
S= pi*(93/360)*13^2=137.16
2(2x+3)=3(3x+1)
Duýdhdhdjjdjdjđm
Answer:
12
Step-by-step explanation:
.......................
Answer:
x=1/2
Step-by-step explanation:
salini's mother's present age is 8 times salini's present age five years from now salini's age will be 1/4th of of his mother's present age what are their present ages
Answer:
salini -= 5 years
mother = 40years
Step-by-step explanation:
[tex]salini = x \\ mother =8x \\ x + 5 = 1 \: of \: 8x \\ x + 5 = 2x \\ 5 = x [/tex]
[tex]5 = x[/tex]
then you equate the values of x
What is the slope of the function? Then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?
Complete question is;
Alejandra correctly wrote the equation y – 3 = (1/5) (x – 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?
Answer:
y – 3 = 2(x – 10)
Step-by-step explanation:
Since the original line is;
y – 3 = (1/5) (x – 10)
This means the slope is 1/5 and the x and y coordinates are (10, 3) respectively.
Now, if she changes the slope to 2 and it still passed through the same point, then it means it's x and y points are still (10, 3). Thus, the equation will now be;
y – 3 = 2(x – 10)
Translate the following into an expression 45% of a
Answer:
Step-by-step explanation:
ok so this is pretty simple,
Imagine a was the number 1
45% of 1, which would obviously be
45/100 * 1
Same thing here but for the variable a.
45/100 * a!
That would be the algebraic expression for 45% of a!
Cheers! I hope you can understand the problem better now.
Which of the following statements is false?
B. A parallelogram is a rectangle.
simplify 3/4×(4)1/3÷(3)1/4
Answer:
The answer is 1
Step-by-step explanation:
3/4×13/3÷13/43/4×13/4×4/13=1What is the equation of the following line? Be sure to scroll down first to see
all answer options.
(0,0)
(-1/2, -3)
O A. y = 2x
O B. y=*
O C. y = 3x
ООО
OD. y = -6x
E. y=-*
OF. y = 6x
Answer:
I think the correct answer is F. y = 6x
We will see that the line equation is y = 6*x
How to find a linear equation?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then we can write the slope as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, the line passes through the points: (0, 0) and (-1/2, -3)
Then the slope is:
[tex]a = \frac{0 - (-3)}{0 - (-1/2)} = 6[/tex]
Then the line is of the form y = 6*x + b
To find the value of b, we use the fact that the line passes through the point (0, 0), then we have:
0 = 6*0 + b
0 = b
We can conclude that the line is y = 6*x
If you want to learn more about linear equations, you can read:
https://brainly.com/question/4074386
It takes Jacob 25 minutes to line 2/3 of the flag football field. At this rate, how long will it take to line the entire field. *
Answer:
12.5 minutes
Step-by-step explanation:
Just divide 25 by 3 to get 12.5
Answer:
37.5 minutes
Step-by-step explanation:
We can set a ratio to model this problem
It takes Jacob 25 minutes to line 2/3 of the flag football field.
The ratio here is 25 : 2/3.
We want to figure out what x : 1 is.
25 : 2/3
x : 1
We can model this by fractions:
[tex]\frac{25}{\frac{2}{3}} = x[/tex]
When you divide by a fraction, you end up multiplying it by the reciprocal.
[tex]25(\frac{3}{2})=x[/tex]
[tex]x=\frac{75}{2}[/tex]
[tex]x = 37.5[/tex]
Which are corresponding pairs
Answer:
pandn
Step-by-step explanation:
jsubeuodoqok1kwnebhxhhw
emdndiiwjwkd
d
ddnjd
Please help me understand
Answer:
B. slope 1/4, y-intercept at ( 0, 5)
Step-by-step explanation:
slope m = change in y /chance in x = 5-4 / 0-(-4) = 1 / 4
the y-intercept is the point where the graph of the line intersects the y-axis so will have the coordinates (0 because x will be 0 if the point is on the y-axis, and y is a number) so is (0, a number)
we are given that one of the points is (x=0, y=5) so this is our y-intercept
OR
the slope intercept form equation of a line y= mx+b, where b is the y-intercept
y = (1/4)x +b, for the point (0, 5) we substitute x=0, and y=5
5 = (1/4)*0 +b
5 = b
The circumference of a circle is 6pi inches. What is the area of the circle
Answer:
B0 A = 9 Pi
Step-by-step explanation:
c = 6 Pi (given)
c = Pi 2r (standard formula)
r = c / (2 Pi)
r = 6 Pi / (2 Pi) = 3 (substitute 6 Pi for c)
So
A = Pi r**2
A = Pi 3**2
A = 9 Pi
find the shaded area...
Answer:
148°
Step-by-step explanation:
The central angle is twice the angle at the circumference, subtended on the same arc.
shaded angle = 2 × 74° = 148°
kiro and lito were assigned the same book to read for a class. kiro started reading on Saturday, and he's reading 20 pages a day. Lito didn't start until Sunday, but he is reading 25 pages a day. How many days will it take Lito to catch up to kiro and how many pages will they have each read?
what system of equations represents this situation and how do you solve it?
A shopkepper marked the price of an articles a csrtain percent above the cost price and he allowed 16% discount to make 5% profit. If a customer paid Rs 9492 with 13% VAT to buy the article by what percent is the marked price above the cost price of the article?
- Hey Risap! :)
[tex] \large{ \tt{❁ \: ANSWER : \boxed{ \tt{25\%}}}}[/tex]
[tex] \large{ \tt{♕ \: REFER \: TO \: THE \: ATTACHMENT \: !!}}[/tex]
Hope this helps! Let me know if you have any questions regarding my answer and also notify me , if you need any other help! :)there are 160 girls and 240 boys in a school
i. find the percent of girls in the school
ii. find the percent of boys in the school.
Answer:
girls = 40%
boys = 60%
Step-by-step explanation:
Girls = 160
boys = 240
total students = 160+240
= 400
so,
percent of girls = (160/400)×100%
= (2/5)×100%
= 2×20%
= 40%
so,
percent of boys = 100% - 40%
= 60%
Which graph has a correlation coefficient, r, closest to 0.95
Answer:
A correlation coeff close to +1 would have a positive slope, and all dots representing the data set would be quite close to the regression line.
Correlation is a measure of association between two variables. IF there is a perfect linear association then correlation would be nearer to 1.
Correlation always lies between -1 and +1.
If between-1 and 0 we say there is a negative correlation.
If nearer to 1 than to 0 then we say strong correlation
Here given correlation is 0.95 i.e. positive and have almost perfect linear relation.
Hence we see that Graph C shows almost linear relationship with slope positive
So option C is answer
I want answer for third question
3rd**
what are the coordinates of vertices of quadrilateral ABCD? use the coordinates to find the length of DA.
A(-5,-4)
B (1,4)
C(4,0)
D(1,-4)
Need help ASAP ???
We can conclude that the length of DA is 6.
For a quadrilateral defined as ABCD, the vertices of the quadrilateral are the points in the name, so the four vertices are the points A, B, C, and D.
These are given, so we know that the vertices are the points:
A(-5,-4)
B (1,4)
C(4,0)
D(1,-4)
Now we want to find the length of DA, this is the distance between points D and A.
Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Then for the case of the points:
A (-5, -4) and D (1, -4)
the distance is given by:
[tex]d = \sqrt{(1 - (-5))^2 + (-4 - (-4))^2} = \sqrt{(1 + 5)^2} = 6[/tex]
Then we can conclude that the length of DA is 6.
If you want to read more, you can see:
https://brainly.com/question/12040665
Slope of (5a, b) and (2a, 2b)
Answer:
8a+4b
Step-by-step explanation:
Givenl || m | n, find the value of x.
. m
44°
77
By
Answer: 0
Submit Answer
attempt 1 out of 2
Can someone pls help
Answer:
x = 136
Step-by-step explanation:
x and 44 are same- side interior angles and sum to 180° , that is
x + 44 = 180 ( subtract 44 from both sides )
x = 136
