The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
What is Parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
Any point on the parabola is equidistant from the focus an directrix.
Distance of a point (x,y) from y=-1 is (y+1)
Distance of a point (x,y) from (4,-7) say L, then
L² = (x - 4)² + (y+7)²
since, L = y + 1
(y + 1)² = (x - 4)² + (y+7)²
y² + 1 + 2y = (x - 4)² + y² + 49 + 14y
-12y - 48 = (x-4)²
-12(y + 4) = (x-4)²
Therefore, The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
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19. What fraction of the distance from M to V is MD?
Answer:the point is located on MV
Step-by-step explanation:
The Coordinates of D (0,-3/4)
If 9x - 3 = 4, what does 9x - 2 = ?
it is given that
9x - 3 = 4
then we can write this
9x - (2+1) = 4
9x - 2 -1 =4
9x - 2 = 4 +1
9x - 2 = 5
so the answer is 5
grant is rolling a six sided number die eight times. How many possible outcomes are there?
The die has 6 faces
[tex]\begin{gathered} \text{ In n number of throws, the number outcomes is given by 6}^n \\ ^{} \end{gathered}[/tex][tex]\begin{gathered} \text{ In 8 throws, the possible outcomes will be 6}^8 \\ =1679616 \end{gathered}[/tex]Evaluate each function in the table at f (3).
Enter the correct answers in the boxes in the table.
Σ
Functions
Function
f(x) = 3x + 5
f(x)=x²-1.5
3
f(x) = 2x
ƒ(3)
The answer to the given functions are:
1) f (3) = 3 × 3 + 5 = 14
2) f( 3 ) = (3)² - 1.5 = 7.5
3) f (3) = 3×2 = 6
What are functions ?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
A function is a type of rule that produces one output for a single input.. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Given : Functions are f(x) = 3x + 5 ------- 1
f(x)=x²-1.5 --------- 2 and f(x) = 2x -----------3
Thus when we put x = 3 we will get the following values that is ;
1 becomes f (3) = 3 × 3 + 5 = 14
and 2 becomes f( 3 ) = (3)² - 1.5 = 7.5
And 3 becomes f (3) = 3×2 = 6
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price. Find the sale price. There are 252 students on the student council at West High School. If there are 700 students enrolled, what percent are on the student council?
We have in total 700 students
252 students are on the students council
700 is 100%
252 is x
x represents the percentage of the student's council, in order to calculate x we need to do the next operation
[tex]x=\frac{252\cdot1}{700}=0.36[/tex]252 is the 36%
the percent of students that are on the student council is 36%
Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
o Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)
o Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)
What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev) /
If the average weight calculated by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
Given that average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows.
We are required to find the margin of error of Val's data.
Margin of error is the difference between the actual data and the calculated data.
Margin of error=1.96*σ/[tex]\sqrt{n}[/tex]
In our case σ=50 and n is 100.
Margin of error=1.96*50/[tex]\sqrt{100}[/tex]
=1.96*50/10
=1.96*5
=9.80
Hence if the average weight calculated by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
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Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 128.
The probability that the IQ is less than 128 is 0.91924
How to determine the probability?The given parameters about the distribution are
Mean value of the set of data, μ = 100Standard deviation value of the set of data σ = 20IQ value, x = 128The z-score of the data value is calculated as
z = (x - μ)/σ
Substitute the given parameters in the above equation
z = (128 - 100)/20
Evaluate
z = 1.4
The probability that the IQ is less than 128 is then calculated as:
P(x < 128) = P(z < 1.4)
From the z table of probabilities, we have;
P(x < 128) = 0.91924
Hence, the probability is 0.91924
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The measure of <1 is greater than 97° and at most 115°. Graph the possible values of x.
Step-by-step explanation:
it help with work
Marbel surveyed 55 people to find out their favorite types of music the results shown in the bar graph
To find the correct option, we need to find, first, the rate of the population that chose each type of music. Then, when we sum the rates of the types in the correct answer, it should result in 40%.
The rate of population for each type of music is given by the number of peaple that chose this type, divided by the total amount of people (55):
Country: 15/55
Jazz: 12/55
Opera: 10/55
Roch: 18/55
In the first option, we have:
Country and Opera
Find the orthogonal trajectories of the family of curves. y^2=6KX^3
The orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]
An orthogonal trajectory of a family of curves is any curve that forms right angles with each member of the family. The curve does not always have to cross each member of the family.
It is given that,
y² = 6Kx³
Differentiate both sides we get,
[tex]\rm 2y = 6k(3x^2) \frac{dy}{dx} \\\\ \frac{dy}{dx} =\frac{2y}{18Kx^2}[/tex]
Substitute the value of K as
[tex]\rm K = \frac{y^2}{6x^3}[/tex]
[tex]\frac{2y}{18(\frac{y^2}{6x^3})x^2} = \frac{dy}{dx} \\\\ \frac{dy}{dx} = \frac{2x}{3y}[/tex]
Consider the negative reciprocal to find the perpendicular slope.
[tex]\frac{-3y}{2x} =\frac{dy}{dx} \\\\ - \int {\frac{1}{2x} \ dx = \int \frac{1}{3y} dy \\\\[/tex]
[tex]-\frac{x^2}{4}+C = \frac{y^2}{6}[/tex]
Simplify,
[tex]\rm 6(-\frac{x^2}{4}+C)= y^2 \\\\ y = \sqrt{6(C-\frac{x^2}{4}}[/tex]
Thus, the orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]
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Among the following which is the best
example for unlike terms?
O8x, 9t
O 9x-2x
О 3р. 5р
All of the choices
Estimate by rounding each number to the nearest ten. Then find the difference.32.76 - 22.168An estimation of the difference isThe exact difference is
ANSWER
EXPLANATION
First let us find the actual difference:
32.76 -
a. Write a formula for the perimeter P of the square.Type your answer into the box below.b. Write a formula for the area A of the square,Type your formula into the box below.
a. The formula for the perimeter of a square is P=4L, where L is the length of it's sides.
b. The formula for the area of a square is A=LxL=L^2, where L is the length of it's sides.
A candy company has decided to sell candy in a new package that is shaped like a triangular prism in order to calculate the volume of the package, the area of the base must be determined.If the base of the package is equilateral triangle with sides 10 centimeters (cm) long, what is the area of the base?
Using the formula for the area of the equilateral triangle, we have:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}a^2 \\ A=\frac{\sqrt[]{3}}{4}(10)^2cm^2\text{ (Replacing)} \\ A=\frac{\sqrt[]{3}}{4}(100)^{}cm^2\text{ (Raising 10 to the power of 2)} \\ A=25\sqrt[]{3}\text{ }cm^2\text{(Dividing 100 by 4}) \\ A=43.3\text{ }cm^2\text{ (Multiplying 25 by }\sqrt[]{3}) \\ \text{The answer is 43.3 cm}^2 \end{gathered}[/tex]Ruben purchases a violin that is on sale for a total price of$1,250, which includes tax and all other fees. He makes aninitial payment of $300 in cash and puts the remainder on hisnew credit card. He makes no other purchases on the card andpays off the credit card balance with 9 monthly payments of$150. What is the difference between the total amount Rubenpays for the violin, including the initial payment and the creditcard payments, and the sale price of the violin?
Given:
Actual price of a violin is $1,250
Credit card monthly payment as $150.
Initial payment is $300.
[tex]\text{Total money paid by Ruben for violin=300+(150}\times9)[/tex][tex]\text{Total money paid by Ruben for violin=300+}1350[/tex][tex]\text{Total money paid by Ruben for violin= \$1650}[/tex]The difference between the total amount Ruben pays for the violin, including the initial payment and the credit card payments, and the sale price of the violin:
[tex]\text{Diffference amount=1650-1250}[/tex][tex]\text{Diffference amount= \$400}[/tex]Difference amount is $400.
you get charged $12.50 for each movie you buy on amazon prime.Somehow you accidentally spent $87.50 on movies last month. How many movies did you buy
You buy seven movies from Amazon Prime which is determined by the division operation.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.
For example 4/2 = 2
A movie ticket costs $12.50 which is given in the question
Last month, $87.50 was spent on Amazon Prime.
Your total movie expenditure is
⇒ 87.50/12.50
Apply the division operation to get
⇒ 7.
As a result, you buy seven movies from Amazon Prime.
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Is y = 2x² a linear or nonlinear function? Please explain.
A linear function has the form:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept, bot constants.
As we see, the exponent of variable x is 1 for a linear function.
So, since the exponent in the given function y = 2x² is 2, this function is a nonlinear function.
In fact, it is a quadratic function.
Which table represents a linear function?
The most appropriate choice for function will be given by-
The first option is correct
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
For the first table,
Slope of function from x = 1 to x = 2
= [tex]\frac{1 - \frac{1}{2}}{2 - 1}[/tex]
=[tex]\frac{1}{2}[/tex]
Slope of function from x = 2 to x = 3
= [tex]\frac{\frac{3}{2}-1}{3 - 2}[/tex]
= [tex]\frac{1}{2}[/tex]
Slope of function from x = 3 to x = 4
= [tex]\frac{2-\frac{3}{2}}{4 - 3}[/tex]
= [tex]\frac{1}{2}[/tex]
Here the slope is same. So the function is linear
For the second table,
Slope of function from x = 1 to x = 2
= [tex]\frac{\frac{1}{2} - 1}{2 - 1}[/tex]
=[tex]-\frac{1}{2}[/tex]
Slope of function from x = 2 to x = 3
= [tex]\frac{\frac{1}{3}-\frac{1}{2}}{3 - 2}[/tex]
= [tex]-\frac{1}{6}[/tex]
Here the slope is not same. So the function is not linear
For the third table,
Slope of function from x = 1 to x = 2
= [tex]\frac{9 - 7}{2 - 1}[/tex]
= 2
Slope of function from x = 2 to x = 3
= [tex]\frac{13 - 9}{3 - 2}[/tex]
= 4
Here the slope is not same. So the function is not linear
For the Fourth table,
Slope of function from x = 1 to x = 2
= [tex]\frac{6 - 0}{2 - 1}[/tex]
=[tex]6[/tex]
Slope of function from x = 2 to x = 3
= [tex]\frac{16 - 6}{3 - 2}[/tex]
= 10
Here the slope is not same. So the function is not linear
So the first option is correct
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Please help me solve this problem it’s my last question on my hw
To solve this problem, we will use the following expression:
[tex]\frac{favorable\text{ outcomes}}{total\text{ outcomes}}.[/tex]In this case:
[tex]\begin{gathered} Total\text{ outcomes}=21+6+6=33, \\ favorable\text{ outcomes}=6. \end{gathered}[/tex]Substituting the above values in the expression, we get:
[tex]\frac{6}{33}.[/tex]Finally, simplifying the above result, we get that the probability that his shirt number is from 67 to99 given that he weighs at most 210 pounds is:
[tex]\frac{2}{11}.[/tex]Answer:
[tex]\frac{2}{11}.[/tex]Write in point-slope form an equation of the line through the pair of points (2,0) and (6,10). Type an equation of the line in point-slope form using one of the given points.
The point-slope form of a line is
[tex]y-y_1=m(x-x_1)_{}[/tex]where (x_1, y_1) are the coordinates of a point on the line.
From the given point we find the slope m.
[tex]m=\frac{10-0}{6-2}=2.5[/tex]With the value of the slope in hand, we now use one of the points given to write down the point-slope form:
[tex]\textcolor{#FF7968}{y-10=2.5(x-6)}[/tex]where we have used the point (6, 10).
What is the solution to this system of equations?X+ 2y = 4| 2x-2y = 5(3.-5)(3.)no solutioninfinitely many solutions
The given system of equation :
x +2y =4
2x -2y =5
On adding both equation we get
x+2y+2x-2y=4+5
3x=9
x=3
So, for y, substitute x=3
x+2y=4
3+2y=4
2y=4-3
2y=1
y=1/2
The solutions is (3,1/2)
The system of linear equation have infintely many solution if they are coincidient, i.e. slope are equal
The given expression :
x+2y =4
2y=4-x
y=(4-x)/2
y = 2-x/2
So slope is (-1/2)
The second equation : 2x-2y=5
2y=2x-5
y=(2x-5)/2
y=x-
What is the distance between three and 11 on the number line
We need to calculate the distance between 3 and 11 on the number line:
[tex]11-3[/tex]That is, from 0 we go 11 units forward and 3 units backward, like this:
Answer: 8
Answer:
8
Step-by-step explanation:
TRIG ANALYSIS- THE LAW OF SINES- THE AMBIGUOUS CASERecall that your triangle should be set up so that angside b, and angle C is opposite side c.PLEASE HELP. WILL MARK BRAINLIEST
The sine law is described by the equation
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]1) Given angle C, length of side b, and length of side c, we are looking for the value of angle B. The angle B can be computed using
[tex]\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \sin B=\frac{b}{c}\sin C \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin B=\frac{34}{31}\sin (65)=0.994 \\ B=\sin ^{-1}(0.994) \\ B=83.7 \end{gathered}[/tex]Thus, angle B is equal to 83.7 degrees.
2) Given angle B, length of side a, and length of side b, we are looking for the value of angle A. The angle A can be computed using
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ \sin A=\frac{a}{b}\sin B \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin A=\frac{10}{5}\sin (126)=1.62 \\ A=\sin ^{-1}(1.62)=Error_{} \end{gathered}[/tex]There are no valid measurements for angle A on this solution.
3) Given angle C, length of side c, and length of side b, we are looking for the value of angle B. The angle B can be computed using
[tex]\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \sin B=\frac{b}{c}\sin C \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin B=\frac{22}{24}\sin (22)=0.3728 \\ B=\sin ^{-1}(0.3728)=21.9 \end{gathered}[/tex]Thus, angle B is equal to 21.9 degrees.
4. Given angle A, length of side c, and length of side a, we are looking for the value of angle C. The angle C can be computed using
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \sin C=\frac{c}{a}\sin A \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin C=\frac{34}{32}\sin (64)=0.955_{} \\ C=\sin ^{-1}(0.955)=72.74 \end{gathered}[/tex]Thus, angle C is equal to 72.74 degrees.
5. Given angle A, length of side c, and length of side a, we are looking for the value of angle C. The angle C can be computed using
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \sin C=\frac{c}{a}\sin A \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin C=\frac{9}{17}\sin (127)=0.4228 \\ C=\sin ^{-1}(0.4228)=25.0 \end{gathered}[/tex]Thus, angle C is equal to 25.0 degrees.
The dimensions of a tennis court are 27 feet by 78 feet. The dimensions of a ping pong table are 9 feet by 5 feet. Is a tennis court a dilation of a ping pong table? Explain why or why not.
Correctly answer yes or no (4 points)
Provide a clear and logical explanation (6 points)
No, The ratios are not equal tennis court is not a dilation of the table.
Given,
The dimensions of a tennis court are 27 feet by 78 feet.
The dimensions of a ping pong table are 9 feet by 5 feet.
To check the:
Is a tennis court a dilation of a ping pong table?
Now, According to the question:
For Tennis Court :
Dimensions is 27feet by 78feet
For Ping Pong Table:
Dimensions is 9 feet by 5 feet
To check that:
27/5 = 27/5 (Take lengths of tennis court and ping pong table )
78/9 = 26/3 (Take breadths of tennis court and ping pong table )
∴ 27/3 ≠ 26/3
Since, No, The ratios are not equal tennis court is not a dilation of the table.
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How do i fill the boundaries for each class? how do i draw a histogram to illustrate this information ? how can i calculate the median age of the population?
Given:
The tabular representation of the data is given.
Required:
Histogram and Median of the given data.
Explanation:
The histogram of the given data is calculated as follows:
Figure 1
The median of the given set of data is calculated as,
Answer:
Thus figure 1 represents the histogram of the given data. The median of the given set of data is 27.7353.
A washer and a dryer cost $935 combined. The washer costs $85 more than the dryer. What is the cost of the dryer?
Answer: $325
Step-by-step explanation:
convert 450 m/s to m/h
1,620,000 m/h
1) To convert 450 m/s we can set out the following:
[tex]\frac{450}{1s}\text{ }\times3600s=1,620,000[/tex]Since 1 hour is equivalent to 3600s then we can simply multiply by 3600 once the unit meter remains the same. m/s to m/h
2) Hence, the answer is 1,620,000 m/h
help me with the 17 pls just give me the answer
Solution
Evaluate each function below for the given equation
17.
[tex]f(x)=11x-9[/tex]f(2) is when the value of x = 2
[tex]\begin{gathered} f(x)=11x-9 \\ f(2)=11(2)-9 \\ f(2)=22-9 \\ f(2)=13 \end{gathered}[/tex]18.
[tex]g(x)=-4(g+2)\text{ for g\lparen5\rparen}[/tex]g(5) is when the value of x = 5
[tex]\begin{gathered} g(x)=-4(g+2) \\ g(x)=-4g-8 \\ g+4g=-8 \\ 5g=-8 \\ g=-\frac{8}{5} \end{gathered}[/tex]19.
[tex]f(x)=3+2(-x)[/tex]
f(-1) is when the value of x = -1
[tex]\begin{gathered} f(x)=3+2(-x)\text{ for x = -1} \\ f(-1)=3+2(-(-1)) \\ f(-1)=3+2 \\ =5 \end{gathered}[/tex]Multiply. Stars and restrictions on the variable. Simplify the rational expression.
Given,
The expression is:
[tex]\frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}[/tex]Required:
The simplified rational expression.
Simplifying the expression,
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}=\frac{x^2+4x-2x-8}{x^2+6x-2x-12}\times\frac{5x+30}{x+5} \\ =\frac{x(x+4)-2(x+4)}{x(x+6)-2(x+6)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)(x-2)}{(x+6)(x-2)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)}{1}\times\frac{5}{x+5} \\ =\frac{5(x+4)}{x+5} \\ =\frac{5x+20}{x+5} \end{gathered}[/tex]Hence, the simplified rational expression is (5x+20)/(x+5).
The restriction of the expression is:
[tex]x\ne-5,\text{ 2,-6}[/tex]
The cheerleading team has won ¾ of their competitions. If the team competes in 16 competitions, how many did they win?
