Find an equation for the parabola that has its vertex at the origin and satisfies the given condition. Directrix y=1/2
Required equation of the parabola with origin as its vertex and directrix
y = 1/2 is equal to x² = -2y.
As given in the question,
Let vertex of the parabola be ( h, k )
Vertex of the given parabola be at origin
⇒ ( h , k ) = ( 0 , 0 )
Directrix is y =1/2 above the vertex.
Focus is ( 0, -1/2)
Equation of the parabola is given by
Distance between focus to the vertex = distance between vertex to the directrix
( y - (1/2) )² = ( x - 0)² + ( y - (-1/2) )²
⇒ y² - y + 1/4 = x² + y² + y + 1/4
⇒ -y = x² + y
⇒x² = -y - y
⇒ x² = -2y
Therefore, the equation of the parabola with vertex at origin and directrix y =1/2 is equal to x² = -2y .
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Graph the function f(x) = 14(0.87). Does this function show growth or decay? What is the equation of the asymptote?
Growth; y = 0
Growth; y = 14
Decay; y = 0
Decay; y = 14
The function f(x) = 14(0.87) has is a constant function has no growth or decay.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given a function f(x) = 14(0.87) Now it is a constant function as for every different values of x the function f(x) has same value and has no growth or decay.
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9. Why is it not possible to make a right triangle using
lengths of 4 feet, 8 feet, and 10 feet? (2 pts)
A 4+8 is greater than 10.
B
10-8 does not equal 4.
C
42+82 does not equal 10².
Answer:
C. 4² +8² ≠ 10²
Step-by-step explanation:
You want to know why it is not possible for the lengths 4, 8, and 10 to form a right triangle.
Pythagorean theoremThe side lengths of a right triangle must satisfy the Pythagorean relation:
a² +b² = c²
These numbers do not:
4² +8² = 16 +64 = 80 ≠ 10² = 100
A right triangle is not formed because ...
4² +8² ≠ 10²
__
Additional comment
The smallest Pythagorean Triple is {3, 4, 5}. Doubling these numbers gives {6, 8, 10}. If the two longest sides are 8 and 10, the shortest must be 6 for a right triangle to be formed.
When the side lengths are reduced to a mutually prime set of numbers, their sum must be even.
4:8:10 reduces to 2:4:5 which has an odd sum.
find the center and radius from the equation (x - 2)^2 + (y + 1)^2 = 16
Answer:
Center: (2,-1)
Radius: 4
Step-by-step explanation:
Circle equation: (x-h)^2 + (y-k)^2 = r^2
Finding the center:
Set to equaling 0 and solve for x and y
(x - 2)^2=0
(y + 1)^2=0
Finding the radius:
In the equation, because it's set to r^2, you would undo the square.
[tex]\sqrt{16}[/tex]=4
Subtract 2w + 4 from 3w - 6
Answer:
w-10
Step-by-step explanation:
(3w-6)-(2w+4)
Take out the brackets:
3w-6-2w-4
Group the like terms:
3w-2w-6-4
Simplify:
w-10
On Kate's reading app, she eams one star for every six books she reads. So far she has read 1.590 booksHow many stars has she earned?
Answer:
265
Step-by-step explanation:
1590/6=265
265x1=265
Which expression is equivalent to (36−y2)
(
36
−
y
2
)
?
Responses
(36+12y+y2)
(
36
+
12
y
+
y
2
)
( 36 + 12 y + y 2 )
(36−12y+y2)
(
36
−
12
y
+
y
2
)
( 36 − − 12 y + y 2 )
(6−y)(6+y)
The equivalent expression to (36 - y²) is (6 - y) (6 + y).
The correct answer option is option C
Which is the equivalent expression?(36 - y²)
Check all options
A. (36 + 12y + y²)
No
B. (36 - 12y + y²)
No
C. (6 - y) (6 + y)
open parenthesis
= 36 + 6y - 6y - y²
= 36 - y²
Yes
D. (6 - y) (6 - y)
= 36 - 6y - 6y + y²
= 36 - 12y + y²
No
In conclusion, the expression (6 - y) (6 + y) is equivalent to (36 - y²)
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Evaluate the absolute of w if w = -8 -5
Answer:
13
Step-by-step explanation:
w = -8 -5 =-13=13
The average cost of a gallon of gas in year one was $2.95. The average cost of a gallon of gas in year two was $2.78. What is the percent of change in the average cost of a gallon from year one to year two? (4 points)
6.2%
6.1%
5.7%
5.8%
the percent of change in the average cost of a gallon from year one to year two is 5.8%
What is average cost change?The term "average cost" refers to the production cost per unit, which is determined by dividing the overall production cost by the overall number of units produced.
The overall cost of production can also be divided into fixed and variable costs. Since total fixed costs often remain constant, changes in total variable costs are the main cause of changes in average costs.
SolutionThe average cost of a gallon of gas in year one was $2.95
The average cost of a gallon of gas in year two was $2.78
The change in the average cost of a gallon from year one to year two is
$2.95 - $ 2.78
⇒$0.17
So percent of change in the average cost of a gallon from year one to year two is
($0.17/$2.95) * 100%
⇒ 0.0576 * 100%
⇒ 5.76%
⇒ 5.8%
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Choose the letter of the correct equation for the graph
Using translation concepts, the equation for the graph is b.
y = cos(x + π/2) + 1
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Suppose that we've got:
f(x) = a cos (bx - c) + d
Then, this function has:
Amplitude (the maximum distance of the graph from the middle line) = a
Period =[tex]\dfrac{2\pi}{b}[/tex]
Phase shift = [tex]\dfrac{c}{b}[/tex]
Maximum value: a + d
Minimum value: -a + d
In this problem, we have a cosine function
(zero at π/2, this is zero at the origin), shifted π/2 units to the right and 1 unit up.
Since the standard amplitude is between -1 and 1, here is between 0 and 2).
Hence the rule is given as follows:
b. y = cos(x + π/2) + 1
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Sonya's heart rate was 76 beats per minute.
She ran a mile on her treadmill and checked
her heart rate again. This time, her heart rate
was 133 beats per minute. What was the
percent increase in Sonya's heart rate?
HELP !!!
Answer: Sonya's heart rate increased by 75% after running a mile on the treadmill.
Step-by-step explanation:
To find the percent increase in Sonya's heart rate, we can use the following formula:
Percent increase = (New value - Old value) / Old value * 100
Substituting the given values into the formula, we get:
Percent increase = (133 beats per minute - 76 beats per minute) / 76 beats per minute * 100
Calculating the result, we get:
Percent increase = 57 beats per minute / 76 beats per minute * 100
= 0.75 * 100
= 75%
Therefore, Sonya's heart rate increased by 75% after running a mile on the treadmill.
The Grinch does not like to talk about his age, But, he does tell people that he is 400 reduced by 2 times his
age is 244. So how old is he really? 78 years old
Answer:88 i think
Step-by-step explanation:
The sequence negative one fifth comma two sixths comma negative three sevenths comma four eighths and so on is given.
Part A: Assuming the pattern continues, list the next four terms in the sequence. Show all necessary math work. (4 points)
Part B: Write the explicit equation for f (n) to represent the sequence. Show all necessary math work. (4 points)
Part C: Is the sign of f (56) positive or negative? Justify your reasoning mathematically without determining the value of f (56). (2 points)
PLEASE ANSWER IN THE FORMAT AS
A;
B;
C;
The answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.
What is a sequence?
A sequence is defined as an arrangement of numbers in a particular order.
A sequence is given ; -1/5, 2/6, -3/7, 4/8.....
Part A
From inspection of the sequence, the pattern is:
i) Add 1 to the numerator of the previous term.
ii) Add 1 to the denominator of the previous term.
iii) Make every other term negative.
Therefore, The next four terms are -5/9, 6/10, -7/11, 8/12
Part B
From inspection of the sequence, we can see that the numerator is the position of the term (n) in the sequence. So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.
The denominator is 5 more than the position of the term in the sequence. So when n = 2 the denominator is 2 + 4 = 6, and when n = 4 the denominator is 4 + 4= 8.
Hence, the rule can be,
f(n) = n/(n+4)
If n is even, then f(n) is positive.
If n is odd, then f(n) is negative.
Part C
56 is an even number.
As the function f(n) is positive when n is even, the sign of f(56) is positive.
Therefore, the answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.
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Solve 9x^2 + 5 = 18x using quadratic formula
Answer:
x= 1/3rd and 5/3rds
Step-by-step explanation:
9x^2 + 5 = 18x
9x^2-18x+5=0
a=9 b=-18 c=6
x=-b+- the Square root of b^2-4ac all over 2a
so x= 18+- the Square root of -18^2 -4x9x5 all divided by 18
x= 18+- the square root of 144 all over 18
so 18+12 over 18 and 18-12 over 18
this simplifies down to x= 5/3 and 1/3
allison uses of a bag of horse feed per day. she feeds 2 quarter horses and 3 paint horses the same amount each day. draw a model to show a whole bag of horse feed below.
Allison feeds 11 horses in a day.
Horses are herbivores and, as such, they need a very specific diet. They must consume lots of fiber to keep their extremely long and sensitive digestive tract working and they must eat little and often, almost all day long.
A horse's feed should consist primarily of grass or roughage. However, hay is insufficient to provide a complete nutritional profile. Important minerals and nutrients will be added by adding grains and concentrates, but calories will also be added. Roughage, feeds, and concentration types are listed below, from least to most "complete."
Given,
Allison feeds 2 quarter horses and 3 paint horses the same amount each day.
Therefore, she feeds 2*4+3 = 11 horses in a day.
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What is 6 3/5-2 7/10
The value of the given expression 6 3/5-2 7/10 is 39/10.
What is an expression?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
Here, we have
Given: 6 3/5-2 7/10
We have to solve this expression and find the value of the given expression.
6 3/5-2 7/10 = 33/5 - 27/10
6 3/5-2 7/10 = (66-27)/10
6 3/5-2 7/10 = 39/10
Hence, the value of the given expression is 39/10.
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the least common multiple of the two numbers is 40 the ratio of the greater number is the to the lessor number is 5, 4
if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.
What is Least Common Multiple (LCM)?Least Common Multiple is the meaning of the abbreviation LCM.
The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.
It can also be computed using two or more numbers.
Finding the LCM of a given collection of numbers can be done in a variety of ways.
Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.
The smallest number among all numbers is called the least common multiple of two or more numbers.
According to our question-
The number LCM is equal to 40.
4 × 5 × x = 40
20 × x = 40
20x=40
x=2
The larger number is equal to 4 x=4(2)=8.
The smaller value is =5x=5(2)=10.
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Complete question-
The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?
Jenny has five exam scores of 100 , 83 , 96 , 84 , and 98 in her biology class. What score does she need on the final exam to have a mean grade of 90 90 ? Round your answer to two decimal places, if necessary. (All exams have a maximum of 100 100 points.)
Jenny needs to score 79 on final exam.
How to add decimal places?A decimal separator is a symbol that separates the integer and fractional parts of a decimal number. Different countries have officially designated various symbols to be used as separators. The symbol chosen also influences the symbol used for the thousands separator in digit grouping. Rounding to two decimal places is the same as rounding to the hundredths place, which is the second place to the right of the decimal point. 2.83620364, for example, can be rounded to two decimal places as 2.84, and 0.7035, to two decimal places as 0.70.
Total marks divide by total number subjects=Average
100+88+96+84+98+x=90*6
461+x=540
x=79
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Closing: What Is the Value of Each Number, and Which Is Larger? Use your teacher’s verbal clues and this number line to determine which number is larger. −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all.
What is a number line?In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.
In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.
As per the given numbers in the number line has been drawn below,
The value of a number in the number line is the absolute value without considering the sign.
For example value of -2 is the distance from zero to -2 so it will be 2.
The largest value is 8 among all numbers.
Hence "The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all".
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Solve the compound inequality and graph on the number lines provided.
7) -2 x ≤ 4 AND 10>-2 x
8) 10<3 x-2 or -3 x-2>14
The compound inequality solved are:
x ≤ 2 and x > -5
x > 4 or x < -5.3
The graph of the number line is given above.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
-2 x ≤ 4 and 10 > -2x
x ≤ 4/-2 and 10/2 > -x
x ≤ -2 and 5 > -x
x ≤ 2 and x > -5
This means.
-5 < x ≤ 2
The number line can be graphed as,
<----__-5__-4__-3__-2__-1__0__1__2__3__4__5----->
o---------------------------------------- o
10 < 3x - 2 or -3x - 2 > 14
10 + 2 < 3x or -3x > 14 + 2
12 < 3x or -3x > 16
x > 4 or -x > 16/3
x > 4 or x < -16/3
x > 4 or x < -5.3
x > 4 can be represented on a line graph as,
__-1__0__1__2__3__4__5__6__7--------->
o----------------------->
x < -5.3 can be represented on a number graph as,
<---------8__-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4---------->
<--------------------------o
Thus,
The compound inequality solved are:
x ≤ 2 and x > -5
x > 4 or x < -5.3
The graph of the number line is given above.
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Which of the following is equivalent to the expression below? √64
-6i
6i
-8i
8i
Answer:
√64 = 8
8i
Step-by-step explanation:
i = √-1
but √64 is a positive number which will produce 8i
Suppose you have just obtained a 30-year home mortgage for $120,000 at an APR of 5%. Find the required monthly payment.
The required monthly payment is given as follows:
$644.22.
What is the monthly payment formula?The monthly payment is defined by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
The parameters are listed as follows:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the values of these parameters are given as follows:
P = 120000, r = 0.05, n = 30 x 12 = 360.
Then:
r/12 = 0.05/12 = 0.004167.
Hence the monthly payment is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 120000\frac{0.004167(1.004167)^{360}}{(1.004167)^{360} - 1}[/tex]
A = $644.22.
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Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $900
Total amount = $1800
Compounded monthly,
so formula becomes,
Total amount = amount (1+r/1200)^12t
T = A[tex](1+r/1200)^{12t}[/tex]
1800 = 900 (1+6/1200)^12t
2 = (1+1/200)^12t
2 = 1.005^12t
taking log on both sides
log 2 = 12t *log 1.005
0.3/0.002 = 12t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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please help me mickey and how do I do brainlest your so smart
Answer:
second option or B
And to mark brainliest on answers when 2 people answer a crown button will appear on the bottom right and you click that
Step-by-step explanation:
-7+4x>-3
+7. +7
4x>4
/4. /4
x>1
So second option is correct
Hopes this helps sorry for late response I was eating
Subtract 81/6-45/6 Simplify the answer and write a mixed number
The value of the given fraction in mixed numbers is 6, or 36/6.
What is fraction?A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a piece or part of a whole. It symbolizes the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator.
Here,
=81/6-45/6
=(81-45)/6
=36/6
=6
The value for given fraction in mixed number will be 6 that is 36/6.
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Write the equation of the line graphed in Point-Slope Form.
Answer: y-3 = -4/5(x+0)
Step-by-step explanation:
formula
y-y1=m(x-x1)
y = y coordinate of the second point
y1 = y coordinate of point one
m = slope
x = x coordinate of the second point
x1 = x coordinate of point one
slope formula
y2-y1/x2-x1
-1-3/5-0
slope = -4/5
the 2 points on the graph are (0,3) (5,-1)
substitute and solve
y-3 = -4/5(x+0)
y-3=-4/5x
How can fossils tell us about Earth's past?
A. Fossils give clues about environmental changes where the organisms lived.
B. Fossils can be used to date the time period of rocks and rock layers when the organisms lived.
C. Fossils can give clues of changes in the organism's body structure over time.
D. All of these are true.
E. None of these are true.
Gwen and Max had breakfast at a cafe. Muffins cost $2 each, and fruit cups cost $4 each. Gwen had 2 muffins and 1 fruit cup. Max had 2 muffins and 1 fruit cup. How much did their breakfast cost?
Answer: Gwen's breakfast in total was $8. Max's Breakfast in total is $8 as well. so their breakfast together is $16 in total
Answer:
their breakfast cost 16 dollars
Step-by-step explanation:
because you would do 2 times 2 which is 4 and 1 times 4 which is also 4 add those two together to get 8 and the double it because max got the same thing
42 minus blank equals 29
Answer: 13
Step-by-step explanation:
Minus 29 from 42 to get 13
Answer:
13
Step-by-step explanation:
If you subtract 20 from 42, you will get your answer. Then you plug it into the equation to make sure it's correct.
42-29=13
29+13=42
42-13=29.
-Hope this helped
A wood state casket labeled 6/6XX would measure in length 6 feet 6 inches and in width
Answer: 28 inches
Hope this helps!!! :)