Answer:
[tex]f(x)=-\frac{1}{16} x^2[/tex]
Step-by-step explanation:
We are to derive the equation of the parabola with a focus at [tex](0, -4)[/tex] and a directrix of y = 4.
We know that a parabola is the locus of all the points as long as the distance from the fixed point on the parabola to the fixed line directrix is kept same.
This parabola is facing downwards. So assuming any point on the parabola to be [tex](x,y)[/tex].
Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]
Distance from [tex](x,y)[/tex] to directrix [tex](y=4)[/tex] = [tex]\left | y-4 \right |[/tex]
Equating these distances as they are equal:
[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |[/tex]
[tex]{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]
[tex]x^2+y^2+8 y +16 = y^2 - 8 y+16[/tex]
[tex]x^2 = -8 y - 8 y= -16 y[/tex]
[tex]x^2= - 16 y[/tex]
So the equation of the parabola is [tex]f(x)=-\frac{1}{16} x^2[/tex].
Answer:
The equation of the parabola is y = -1/16 x²
Step-by-step explanation:
* Lets revise some facts about the parabola
- Standard form equation for a parabola of vertex at (0 , 0)
- If the equation is in the form x² = 4py, then
- The axis of symmetry is the y-axis, x = 0
- 4p equal to the coefficient of y in the given equation to
solve for p
- If p > 0, the parabola opens up.
- If p < 0, the parabola opens down.
- Use p to find the coordinates of the focus, (0 , p)
- Use p to find equation of the directrix , y = - p
* Lets solve the problem
∵ The focus at (0 , -4)
∵ The coordinates of the focus are (0 , p)
∴ p = -4
∵ The directrix is y = 4
∵ The equation of the directrix , y = - p
∴ -p = 4 ⇒ p = -4
∵ the equation is in the form x² = 4py
∵ p = -4
∴ x² = 4(-4)y
∴ x² = -16y ⇒ divide both sides by -16
∴ y = -1/16 x²
* The equation of the parabola is y = -1/16 x²
If you have an average 90. Give two numbers other than 90 that would make the average 90
Answer:
The numbers 180 and 0 would make the average 90
Step-by-step explanation:
we know that
To find the average of two numbers, add the numbers and then divide by two.
Let
x ----> one number
y ----> the other number
The average is equal to
(x+y)/2
For x=180 and y=0
the average is equal to
(180+0)/2=90
therefore
The numbers 180 and 0 would make the average 90
the set of ordered pairs represented by the graph below can be described as which of the following
a relation only
a function only
both a relation and function
neither a relation or function
ANSWER
a relation only
EXPLANATION
The given graph shown in the attachment represents only a relation and not a function.
The reason is that, a vertical line drawn across this graph will intersect this graph at more than one point.
Since the graph fails to pass the vertical line test, the ordered pair represented by this graph represents a relation only.
Answer: First option.
Step-by-step explanation:
By definition, a relation is a function if each input value (value of "x") has only one output value (value of "y").
In the figure you can observe that each x-coordinate has more than one y-coordinate. Then, since each input value (value of "x") does not have only one output value (value of "y"), you can say that it is not a function, but a relation only.
Therefore, the conclusion is:
The set of ordered pairs represented by the graph, can be described as a relation only.
10. One number is 5 times another number, and
their sum is -60. What is the lesser of the two
numbers?
F. -5
G. -10
H. -12
1 -48
Answer:
G. -10
Step-by-step explanation:
Let one number = x
Let the second one = y
Equations
y = 5x
x + y = -60
Solution.
Put 5x in for y in the second equation.
x + 5x = -60 Combine like terms on the left
6x = -60 Divide by 6
6x/6 = -60/6 Do the division
x = -10
So one of the numbers is minus 10
Train A arrives at the station at 11:50 AM and leaves the station at 1:50 PM. How long does it stay in the station?
Make a Selection:
A. 1 hr
B. 1 hr 25 min
C. 2 hrs
D. 10 hrs
Answer:
C. 2 hrs
Step-by-step explanation:
11:50am + 1 hour = 12:50pm
12:50 pm + 1 hour = 1:50 pm
9 to the third power
Answer:
729
Step-by-step explanation:
9 x 9 x 9
Answer:
729
Step-by-step explanation:
9^3=9×9×9. 9×9=18. 18×9=729.
Plane H is shown.
Which points are coplanar and noncollinear?
Answer:
points A, B, and D
Step-by-step explanation:
f(x) = 4x2 + 1 and g(x) = x2 - 5, find (f+ g)(x)
Answer:
Step-by-step explanation:
(f + g)x translates into a more readable f(x) + g(x) so all you do is
f(x) + g(x) = 4x^2 + 1 + x^2 - 5
f(x) + g(x) = 5x^2 - 4
Answer:3x^2+6
Step-by-step explanation: I'm not really good at math but the correct answer is 3x^2+6
What value of x is in the solution set of 3(x-4)>5x+2?
3(x - 4) > 5x + 2
First you must distribute the 3 to the numbers inside the parentheses
(3 * x) + (3 * (-4)) > 5x + 2
3x + (-12) > 5x + 2
3x - 12 > 5x + 2
Now you must combine like terms
3x goes with 5x
^^^To do this subtract 3x to both sides of the equation
(3x - 3x) - 12 > (5x - 3x) + 2
0 - 12 > 2x + 2
-12 > 2x + 2
-12 goes with 2
^^^To do this subtract 2 to both sides
-12 - 2 > 2x + (2 - 2)
-14 > 2x + 0
-14 > 2x
Isolate x by dividing 2 to both sides
-14/2 > 2x/2
-7 > x
Hope this helped!
~Just a girl in love with Shawn Mendes
Try hard to do
This one please
Answer:
Runner D
Step-by-step explanation:
The coach has her team run at least 60 miles per week. What is the letter of the runner who has completed 0.25 of the weekly distance. 0.25×60=15
convert 9.25% to fraction form
Answer:
[tex]\frac{37}{400}[/tex]
Step-by-step explanation:
9.25% as a fraction would be [tex]\frac{9.25}{100}[/tex], since a percentage is always out of 100.
Multiply the fraction by 100 to convert the decimal into fraction form
[tex]\frac{9.25}{100} \rightarrow\frac{925}{10000}[/tex]
Reduce to the simplest terms
[tex]925\div25=37\\\\ 10000\div25=400\\\\ \frac{37}{400}[/tex]
the national flag of scotland has a white diagonal on a blue backround Tracy is sewing a scottish flag she knows that the length of one diagonal will be 15 feet and the flag will be 9 feet high to the nearest foot how long will the scottish flag be
Answer:
12 feet
Step-by-step explanation:
By Pythagoras theorem, a²+b²=c², where c represents the diagonal and a and b represents the other sides of a right angled triangle
As a flag is a rectangle, the two triangles cut would be right angled triangles
Therefore, a²+9²=15²
a²+81=225
a²=144
a=√144
a=12 feet
Final answer:
To calculate the length of the Scottish flag, the Pythagorean theorem is applied. With a diagonal (hypotenuse) of 15 feet and a height of 9 feet, the length is found to be 12 feet.
Explanation:
The question involves calculating the length of the Scottish flag given the length of one diagonal and the flag's height. To find the length of the Scottish flag, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, we know the length of the diagonal (hypotenuse) is 15 feet and the height (one side) is 9 feet.
Let x be the length of the Scottish flag (the other side of the right-angled triangle). According to the Pythagorean theorem, [tex]x^2 + 9^2 = 15^2.[/tex]
Solving for x, we get:
[tex]x^2 + 81 = 225[/tex][tex]x^2 = 225 - 81[/tex][tex]x^2 = 144[/tex][tex]x = \sqrt144[/tex]x = 12Therefore, the length of the Scottish flag will be 12 feet to the nearest foot.
What equation has the steepest graph ?
Answer:
B
Step-by-step explanation:
for a linear equation y = mx + b,
the steepness of the graph is denoted by the slope, m
The larger the absolute number of the slope, the steeper it is
in this case it is quite clear that B has the largest absolute number for m.
i.e abs (-10) = 10
It is about a 425-mile drive from San Jose to
Los Angeles down CA-1, and about a 320-
mile drive from San Jose to Santa Barbara
along the same route.
If you stop in Santa Barbara, you can take a
walk along the water front, or visit the Santa
Barbara Zoo.
How far is the drive from
Santa Barbara to Los Angeles?
Answer:
105
Step-by-step explanation:
425 - 320 = 105 miles
Final answer:
The drive from Santa Barbara to Los Angeles is 105 miles, which is the difference between San Jose to Los Angeles (425 miles) and San Jose to Santa Barbara (320 miles).
Explanation:
The question asks how far it is to drive from Santa Barbara to Los Angeles. To determine this distance, we utilize the total distance from San Jose to Los Angeles and subtract the distance from San Jose to Santa Barbara. Starting with the overall distance of San Jose to Los Angeles, which is 425 miles, we deduct the San Jose to Santa Barbara distance of 320 miles. This calculation will provide us with the distance from Santa Barbara to Los Angeles.
By subtracting 320 miles from 425 miles, we find that the distance from Santa Barbara to Los Angeles is 105 miles.
Alex completed 7 homework problems in class. The function p(m) relates the
time (in minutes) Alex spent on his homework at home to the total number of
problems he completed. The input is the number of minutes worked. The
output is the number of problems completed.
p(m)=m/4+7
Which equation represents the inverse function m(p), which uses problems
completed as the input and gives minutes worked as the output?
The answer is:
D. [tex]m(p)=4p-28[/tex]
Why?Inversing a function consists of switching the function (name) and the variable, so, where we have the variable (m for this case) we should rewrite it as the function (p(m)), and then, isolate the function in order to know the inverse function.
So, we are given the function:
[tex]p(m)=\frac{m}{4}+7[/tex]
We know that:
[tex]p(m)^{-1}=m(p)[/tex]
Then, rewriting and calculating, we have:
[tex]p(m)=\frac{m}{4}+7[/tex]
[tex]p=\frac{m(p)}{4}+7\\\\p-7=\frac{m(p)}{4}\\\\m(p)=(p-7)*4=4p-28[/tex]
Hence, we have that the answer is:
D. [tex]m(p)=4p-28[/tex]
Have a nice day!
Charles is on a 8 1/2 mile bike ride. He stops for a rest after he’s gone 5 2/5 miles. How much farther does he still have to go?
Answer:
31/10 or 3 1/10 more miles.
Step-by-step explanation:
=
(17 × 5) - (27 × 2)
2 × 5
Answer:
[tex]3\frac{1}{10}[/tex] miles
Step-by-step explanation:
The total distance of Charles bike ride is = [tex]8\frac{1}{2}[/tex] miles
He has covered the distance = [tex]5\frac{2}{5}[/tex] miles
We will subtract his covered distance from total distance.
He still have to go = [tex]8\frac{1}{2}[/tex] - [tex]5\frac{2}{5}[/tex]
= [tex]\frac{17}{2}[/tex] - [tex]\frac{27}{5}[/tex]
= [tex]\frac{85-54}{10}[/tex]
= [tex]\frac{31}{10}[/tex]
= [tex]3\frac{1}{10}[/tex] miles
He still have to go [tex]3\frac{1}{10}[/tex] miles
If x+4/4 =y+3/3 then y/3=
Answer:
x/4
Step-by-step explanation:
(y+3)/3=y/3+3/3=y/3+1
So to find y/3 in your equation all we would need to do is subtract 1 on both sides giving:
(x+4)/4-1
This can be simplified
x/4+4/4-1
x/4+1-1
x/4+0
x/4
Answer: x/4
x2+4x+6
a.f(-8) b. f(x+4) c.f(-x)
Answer:
a. f(-8) = 38b. f(x + 4) = x² + 12x + 38c. f(-x) = x² - 4x + 6Step-by-step explanation:
[tex]f(x)=x^2+4x+6\\\\a.\\f(-8)-\text{put x = -8 to the equation}\\\\f(-8)=(-8)^2+4(-8)+6=64-32+6=38\\\\b.\\f(x+4)-\text{exchange x to x + 4}\\\\f(x+4)=(x+4)^2+4(x+4)+6\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and}\ \text{distributive property}\\\\f(x+4)=x^2+2(x)(4)+4^2+4x+(4)(4)+6\\\\f(x+4)=x^2+8x+16+4x+16+6\\\\\text{combine like terms}\\\\f(x+4)=x^2+(8x+4x)+(16+16+6)\\\\f(x+4)=x^2+12x+38[/tex]
[tex]c.\\f(-x)-\text{exchange x to -x}\\\\f(-x)=(-x)^2+4(-x)+6=x^2-4x+6[/tex]
At the beginning of March, Janet opened a checking account with her first paycheck of $153.82. During the month, she withdrew $40 from the ATM, wrote a check for $54.12 to pay for her cell phone, deposited a check for $215.70, transferred $75.00 to her savings account, and had a debit of $130 for sports equipment.
Answer:
$ 70.4
Step-by-step explanation:
Data:
The opening balance = $ 153.82
Withdrawal made = - $ 40
Check for payment = - $ 54.12
Deposited a check for payment = + $ 215. 70
Transferred amount to the savings = - $ 75.00
Debit for the sports equipment = -$ 130
The total amount left will be = $ (153.82- 40-54.12+ 215.70-75-130)
= $ 70.4
Answer:
The account balance is $70.40.
Explanation:
Please make the brainliest :)
Somebody help this is algebra
Answer:
2 is your answer
Step-by-step explanation:
If h(x)= 5 then 5= 2x +1
so 5 = 2x + 1
-1 -1 on both sides
then 2x = 4
2 2 divide by 2
which x = 2
Hope my answer has helped you!
Lin multiplies 7/8 times a number.the product is less than 7/8 . Which could be Lin’s number ?
Answer:
Any number less than 1
Step-by-step explanation:
Let x be the number Lin multiplies by 7/8. So, we have:
(7/8)*x < 7/8
We need to find the possible values for x. Lets start by dividing both sides of our inequality by (7/8) in order to get x alone on the left side.
(7/8)*x / (7/8) < (7/8)/(7/8)
Reordering:
(7/8) / (7/8) * x < (7/8)/(7/8)
As any number divided by itself (except from 0) is equal to 1:
x < 1
So, the number that Lin multiplied by 7/8 MUST be less than 1. This is evident, as any positive number multiplied by a number less than 1 will decrease, doesn't matter if its a negative or positive number.
So, such number is less than 1. Any number less than 1 could be Lin's number.
Which table of ordered pairs represents a proportional relationship?
Answer:
The correct option is 3.
Step-by-step explanation:
We need to find a table of ordered pairs that represents a proportional relationship.
Proportional relationship: It means y-values are proportional to x-values.
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
For table 1,
[tex]\frac{y_1}{x_1}=\frac{8}{4}=\frac{2}{1}[/tex]
[tex]\frac{y_2}{x_2}=\frac{11}{7}[/tex]
[tex]\frac{2}{1}\neq \frac{11}{7}[/tex]
Table 1 does not represents a proportional relationship.
Similarly,
For table 2,
[tex]\frac{25}{5}\neq \frac{49}{7}[/tex]
Table 2 does not represents a proportional relationship.
For table 3,
[tex]\frac{3}{6}=\frac{5}{10}=\frac{7}{14}=\frac{1}{2}[/tex]
Table 3 represents a proportional relationship.
For table 4,
[tex]\frac{6}{3}\neq \frac{11}{8}[/tex]
Table 4 does not represents a proportional relationship.
Only table 3 represents a proportional relationship. Therefore the correct option is 3.
The digits 1,2,3 and 4 are used to make a 3 digit number. Each digit can be repeated. What is the total number of 3 digit numbers that can be made using these digits?
Answer:
24 ways
Step-by-step explanation:
4P3 = 4*3*2
=24
Final answer:
The total number of three-digit numbers that can be made using the digits 1, 2, 3, and 4 with repetition allowed is 64. This is computed by multiplying the number of digit options available for each place value in a three-digit number (4 options each for hundreds, tens, and ones).
Explanation:
To determine the number of possible three-digit numbers that can be created using the digits 1, 2, 3, and 4, with the possibility of repeating digits, we need to consider that each place value (hundreds, tens, and ones) can be filled by any of the four digits available.
Therefore, for the hundreds place, there are 4 options (1, 2, 3, or 4). The same is true for the tens and ones place, since repetition is allowed, giving 4 options for each. We calculate the total number of combinations by multiplying the number of options for each place value:
Hundreds place: 4 options
Tens place: 4 options
Ones place: 4 options
The total number of possible numbers is 4 (for the hundreds) × 4 (for the tens) × 4 (for the ones) = 64 numbers.
if the diameter of a circle is 7/8 of an inch what is its radius
Answer:
r = 7/16 inch
Step-by-step explanation:
The radius is 1/2 of the diameter
r = 1/2 d
r =1/2 (7/8)
r = 7/16 inch
Vanesa earns a base salary of $400.00 every week with an additional 5% commission on everything she sells. Vanessa sold $1650.00 worth of items last week.
What was Vanessa’s total pay last week?
Answer:
$482.50
Step-by-step explanation:
x=1650×5/100
x=16.5×5
x=82.50
400+82.5=482.5
Answer:
482.50
Step-by-step explanation:
Her base is 400. If she sells nothing, that's her take home.
Take home = 400 + 5% of what she sells.
Take home = 400 + (5/100) * 1650
Take home = 400 + (0.05) * 1650
Take home = 400 + 82.50
Take home = 482.50
In an '80% off' sale, an oven was £112. Work out the original price.
Answer:520
Step-by-step explanation:
Suppose the original prize is=x
If the discount is of 80%,the selling prize is of 20%
20% of x=112
20x/100=112
X=520
Its the original prize...
Answer:
£560
Step-by-step explanation:
80% off means that the sale price is 20% of the original price.
The original price is represented by 100%
Divide the sale price by 20 to find 1% then multiply by 100 to obtain the original price
original price = [tex]\frac{112}{20}[/tex] × 100 = £560
Based only on the given information, it is guaranteed that PS=RS
PLS HELP ASAP
Answer: True :)
Step-by-step explanation:
Simplify the expression –3(x + 3)2 – 3 + 3x. What is the simplified expression in standard form?
–3x2 – 18x – 27
–3x2 – 15x – 30
–3x2 + 3x + 6
–3x2 + 3x – 30
Answer:
[tex]-3x^2-15x-30[/tex]
Step-by-step explanation:
The given expression is [tex]-3(x+3)^2-3+3x[/tex].
We expand to obtain:
[tex]-3(x^2+6x+9)-3+3x[/tex].
We apply the distributive property to get:
[tex]-3x^2-18x-27-3+3x[/tex].
Group and combine the like terms;
[tex]-3x^2-18x+3x-27-3[/tex].
[tex]-3x^2-15x-30[/tex].
This polynomial expression is in standard form because it is descending powers of x.
The simplification of the algebraic expression in standard form is -3x² - 15x - 30
What is an algebraic expression?An algebraic expression is the expression of mathematical variables with their coefficients(numbers), integers, and arithmetic operations. The simplification of algebraic expression usually follows a pattern such as;
opening the bracketstaking like terms and solving the like terms separately.From the given algebraic expression, we have:
= -3(x + 3)² - 3 + 3x
Let's expand the above terms in the bracket, we have:
= -3(x² +6x + 9) - 3 + 3x
= -3x² - 1x - 27 - 3 + 3x
By rearrangement, we have:
= -3x² - 18x + 3x - 27 - 3
= -3x² - 15x - 30
Learn more about algebraic expression here:
https://brainly.com/question/4344214
Evalute 12/y + 9z for y=6 and z=3
Answer:
29
Step-by-step explanation:
12/6 + 9(3) = 2 + 27 = 29
Answer:
29
Step-by-step explanation:
Use the substitution method to solve the system of equations. Choose the correct ordered pair. 2x + y= 8 and y= -x + 5
Answer:
The ordered pair is (3, 2).
Step-by-step explanation:
y = -x + 5
2x + y = 8
Substitute y = -x + 5 in the second equation:
2x + (-x + 5) = 8
x + 5 = 8
x = 3.
Now substitute x = 3 into the first equation;
y = -3 + 5
y = 2.
What is the solution to
y=-3x + 6
y = 9
(-21, 9)
O (9,-21)
• (-1,9)
(9, -1)
Answer:
(-1,9)
Step-by-step explanation:
y=-3x + 6
y = 9
We know that y=9
Substitute that into the first equation
9 = -3x+6
Subtract 6 from each side
9-6 = -3x+6-6
3 = -3x
Divide by -3
3/-3 =-3x/3
-1 =x
x=-1, y=9
(-1,9)