Equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).
As given in the question,
Focus of the parabola is equal to (-3, -3)
Directrix of the parabola is given by x = 5
Let (x, y) be the point on the parabola.
Distance between the (-3,-3) and (x, y) = Distance between (x, y) and x=5
⇒√(x +3)² + (y +3)² = | x -5|
⇒(x² +6x +9) +(y² + 6y +9) = (x-5)²
⇒x² +6x +y² +6y +18 = x² -10x +25
⇒y² +6y -7 = -16x
⇒x = (-1/16) (y² +6y -7) represents the equation of the parabola.
Therefore, equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).
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PLS HELPP TYSM I NEED HELP ASAPPPP
Answer:
x = 7
Step-by-step explanation:
(10x+30)° and (17x-19)° are
EQUAL TO EACH OTHER
10x+30 = 17x-19
7x = 49
x = 7
desmos
an insurance company wants to study whether offering incentives for preventative care reduces overall health care costs. they select a random sample of 200200200 of their customers. they use a random number generator to select 100100100 customer account numbers to offer the incentive. the remaining 100100100 customers are assigned to the control group. what type of experiment design is this?
Using the concepts of probability, we got that that Stratified sampling is the experiment design which an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs.
In the question, actually the insurance company intends to study and understand the relationship between the health care cost of the customers and the provision of incentives for the preventative care by two groups, each having one of two given attributes under study, which are;
a) One group consist of the customers having high health care cost and offered incentives for preventative care
b) The other group consist of the customers having only high health care cost without incentives
Therefore, the insurance company customers are stratified into the groups based on health care cost and again into the groups that have high health care cost and are offered preventative care and those that have only the high heath care cost, which is the process used to implement the stratified sampling technique.
Hence, an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs, by selecting a random sample of 200200200 of their customers and using a random number generator to select 100100100 customer account numbers to offer the incentive, the experiment design is named as Stratified sampling.
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a data analyst is using statistical measures to get a better understanding of their data. what function can they use to determine how strongly related are two of the variables?
The correlation coefficient can be used to get a better understanding and to determine the extent of a strong relation between two variables.
In a statistical setting, two or more variables are said to be connected if their values fluctuate in such a way that as the value of one variable rise or falls, the value of the other variable does the same (although it may be in the opposite direction).
For instance, there is a relationship between the two variables "hours worked" and "revenue earned" if a rise in hours worked is correlated with an increase in income earned. When considering the two factors "price" and "purchasing power," the ability of a person to purchase items reduces as the price of those goods rises (assuming a constant income).
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HELP!!!!!
A state offers specialty license plates that contain 3 letters followed by 2 numbers. License plates are assigned randomly. All license plates are equally likely. Find the number of possible license plates that can be issued using this system.
17,576,000 possible license plates
1,757,600 possible license plates
36 possible license plates
98 possible license plates
The number of possible license plates that can be issued using this system is 1757600. Therefore, option B is the correct answer.
Given that, a state offers specialty license plates that contain 3 letters followed by 2 numbers.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
The number of possible license plates
= 26×26×26×10×10
= 1757600
The number of possible license plates that can be issued using this system is 1757600. Therefore, option B is the correct answer.
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how does the symmetry of a parabolas hep you graph a quadratic function?
The axis of symmetry is the line that is relative is vertical goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line that is relative the graph of a equation that is quadratic two mirror images.
Equation of the Axis of Symmetry of a Parabola:
The equation for the axis of symmetry of a parabola can be expressed as:
[tex]x=\frac{-b}{2a}[/tex]
Remember that every quadratic function can be written in the standard form [tex]y = ax^{2}+bx+c[/tex] . The graph of a quadratic function is called a parabola, where every point on that parabola represents an x and a y that solves the quadratic function.
The vertex of a quadratic function is the highest or lowest point on the graph. The coordinate of the vertex of the parabola, then, is the x and y solution for the lowest or highest point of the parabola.
Calculating the Axis of Symmetry of a Parabola:
Again, the axis of symmetry of the parabola is the line on the graph that passes through the vertex of the parabola and splits the graph into two symmetrical sides.
It is expressed as:
[tex]x=\frac{-b}{2a}[/tex]
Or x = -2 after you substitute in the values for a and b.
Finding the Vertex of a Parabola:
To find the actual coordinates for the vertex of the parabola, simply substitute the x value into the polynomial expression to find the corresponding y value. Remember, each point on the quadratic graph is a solution to the equation.
When we continue with the previous example, we know that x = -2.
We substitute that value for x in the original quadratic function.
[tex]y=x^{2} +4x+3\\y=(-2)^{2}+4(-2)+3\\ y=4+(-8)+3[/tex]
Solving it gives us y = -1. We now know that the vertex of the parabola is the coordinate (-2, -1). Finding the vertex of a parabola couldn’t be easier.
How To Find Axis of Symmetry?
Here's what you need to remember: Whether you’re after the axis of symmetry or the full coordinates of the vertex of the parabola, use this formula to start graphing a quadratic equation.
[tex]x=\frac{-b}{2a}[/tex]
Solving for x gives you the axis of symmetry. This line of symmetry will intersect with the parabola at its vertex, where x is the coordinate you just calculated and y is the coordinate when you substitute x back into the quadratic equation,
[tex]y = ax^{2}+bx+c[/tex].
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10p^2 - 20p - 34 = -4
Answer:
p = -1 ; p= 3
Step-by-step explanation:
10p^2 - 20p - 34 +4 = 0
10p^2 -20p - 30 = 0
10/10 p^2 - 20/10 p - 30/10 = 0
p^2 - 2p - 3 = 0
(p-3)(p+1) = 0
p = 3
p = -1
Lola’ mom walked x feet and then half that length agin how many feet did Lola’ mom walk
Total( as there is addition) feet walked by Lola is 29.25 +1.5x for the given equation.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division.
Main body:
Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:
= 10 + (1/2 × 10) = 10 + 5 = 15 feet
Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:
= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet
Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:
= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75
Lola's mom walked x feet, and then half that length again. Total length walked will be:
= x + (1/2 × x) = x + 0.5x = 1.5x
Total feet walked by the whole member of the family will be:
= 15 + 4.5 + 9.75 + 1.5x
= 29.25 + 1.5x
Hence Total feet walked by Lola is 29.25 +1.5x for the given equation.
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A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and
food tickets cost $3.25 each. The family pays a total of $90 for the tickets.
store.
The number of ride tickets that were sold are 8 and the number of food tickets that were sold are 24 .
In the question ,
it is given that
total number of tickets bought by the family at carnival = 32 tickets
total amount spent by the family of tickets = $90
let the number of ride tickets be [tex]=[/tex] x
let the number of food tickets be [tex]=[/tex] y
So , x + y = 32
x = 32 - y
cost of 1 ride ticket = $1.50
cost of 1 food ticket = $3.25
So the total cost is 1.25x + 3.25y = 90
Substituting x = 32 - y in the equation 1.5x + 3.25y = 90 ,
we get ,
1.5(32 - y) + 3.25y = 90
48 - 1.50y + 3.25y = 90
1.75y = 90 - 48
1.75y = 42
y = 24
So , x = 32 - 24 = 8
Therefore , The number of ride tickets that were sold are 8 and the number of food tickets that were sold are 24 .
The given question is incomplete , the complete question is
A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and food tickets cost $3.25 each. The family pays a total of $90 for the tickets store. How many of each type of ticket were sold ?
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Use the power of a power property to select each correct way to rewrite the expression x15
The correct way by using the power of a power property we can write as;
⇒ x¹⁵ = (x³)⁵
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ x¹⁵
Now,
Since, The expression is,
⇒ x¹⁵
We can write the expression as by using the power of a power property as;
⇒ x¹⁵ = (x³)⁵
Thus, The correct way by using the power of a power property we can write as;
⇒ x¹⁵ = (x³)⁵
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Which graph shows how to graph a line with a slope of 3 and y intercept of -2
The equation of the line is y=3x-2 where the slope is 3 and the y-intercept is -2.
What is meant by the graph?A diagrammatic depiction of a set of facts is called a graph, chart, or diagram.
Graphs need to be accurate and effective in communicating information. They ought to be legible at different computer screen resolutions. Graphs should ideally be pleasing to the eye.
Please be aware that the terms graph, chart, and diagram can be imprecise and are sometimes used synonymously.
Graphs need to be accurate and effective in communicating information. They ought to be legible at different computer screen resolutions.
Given,
Slope m=3
y-intercept (c)=-2
The slope-intercept form is given as
y=mx +c
Therefore, y=3x-2
The equation of the line is y=3x-2 where the slope is 3 and the y-intercept is -2.
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An angle is bisected. Each resulting angle is 78 degree. how is the original angle
A plane is on its approach to land on the runway. The jet's height above the ground is given in feet as a function of
the time in seconds. The following table tracks the plane as it lands:
t (in seconds) h (in feet)
0
4000
5
3500
10
3000
15
20
25
2500
2000
1500
Mark this and return
=
Ah
4
Calculate the slope. Use the formula
a. The plane is losing altitude.
b. The plane is gaining altitude.
c. The plane is remaining at a constant height.
d. The plane is losing altitude at a rate of 500 feet/second.
At
What is the significance of the sign of the slope?
Save and Exit
Next
Submit
The slope Using the formula will be h = -100t + 4000
This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line.
If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept.
If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.
Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:
h = -100t + 4000 which appears to be choice a.
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The points K, L, M and N all lie on the same line segment, in that order, such that the ratio of KL:LM:MNKL:LM:MN is equal to 2:3:1.2:3:1. If KN=54,KN=54, find MN.MN.
The length of the line segment MN given that the ratio of KL:LM:MN = 2:3:1 is; 9
How to carry out partitioning of line segment?
We are told that the points K, L, M and N all lie on the same line segment.
Since the points lie on the same line segment, then it means that they are collinear points.
We are told that the ratio of the segments, KL:LM:MN = 2:3:1.
This means that we can find the length of MN since we are also given the total length of the whole segment, KN = 54.
Length of MN = (Individual ratio of MN ÷ the total ratio value of the 3 given segments) × length of the whole segment
Individual ratio of MN = 1
Total ratio value of the 3 given segments = 2 + 3 + 1 = 6
Length of whole segment, KN = 54
Length of MN = (1/6) * 54
Length of MN = 9
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A company is expanding its building area from 12,500 square feet to 16,875 square feet. What is the percentage increase of the area of the building space?
A. 35%
B. 65%
C. 43.75%
D. 3.5%
The percentage increase in the area of the building from its initial space is 35% of the increase. Hence, option A is correct.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the data provided in the question,
The initial area of the building = 12,500
Increase in area of building = 16875
The percentage increase in the area will be,
% increase = (16875 - 12500)/12500 ×100
⇒ 4375/12500 × 100
% increase = 35%
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Williams and Co. is spliting their stock at a ratio of 3:1. The pre-split price is $43.25 and the pre-split number of shares is 2.5 million. What is their Total pre-split Market Capitalization?
Total pre-split Market Capitalization is $1,08,125,000.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
Williams and Co. is splitting their stock at a ratio of 3:1. The pre-split price is $43.25 and the pre-split number of shares is 2.5 million.
Total Value of Shares = $43.25 Share Price × 2.5 × 10⁶ Shares
Total Value of Shares = $1,08,125,000
Let’s say the company’s board decides to approve a 3-for-1 split.
Total Shares = 2.5 × 10⁶ × 3 = 75,00,000
Share Price = $43.25 ÷ 3 = $14.416
Total Value of Shares = $14.416 Share Price × 75,00,000 Shares
Apply the multiplication operation,
Total Value of Shares = $1,08,120,000
Thus, the total pre-split Market Capitalization is $1,08,125,000.
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Select the two values of x that are roots of this equation. x2 + 3x – 5 = 0
The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
What are the two values of x which are root of the given quadratic equation?It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.
Recall that the roots of quadratic equations are given by the formula;
x = {-b ± √(b² - 4ac)} / 2a
Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.
Therefore, the roots are as follows;
x = {-3 ± √(3² - 4•1•-5)} / 2(1)
x = (-3 ± √29)/2
Therefore, the required roots are;
x = (-3 + √29)/2 and x = (-3 - √29)/2
Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
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the p-value is a. a sample statistic. b. the same as the z statistic. c. a distance. d. a probability.
The p - value is d ) a probability .
Defining P - Value
P - Value : It is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test , assuming that the null hypothesis is correct . The p - value does not , in itself , establish probabilities of hypotheses . Rather , it is a tool for deciding , whether to reject null hypothesis or not .
A smaller p - value means that there is stronger evidence in favor of alternative hypothesis .
Hence , the p - value is d ) a probability .
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1) suppose the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane. how many possible states are there? how many paths are there to the goal? provide assumptions for your answer
There will be infinite number of states and paths when the state space is (x,y) as the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane.
What is state space?The collection of every possible setup for a system is its state space. It is a common abstraction in the study of artificial intelligence and game theory because it can be used to reason about the behavior of a specific system. A state space is typically introduced into a system description without being given any thought to its precise physical meaning. However, it is well known that choosing an appropriate state space representation makes it simpler for us to comprehend or control a system's property.
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What is the diameter of a circle with a circumference of 47.1 in.?
A. 7.5 in.
B. 15 in.
C. 0.75 in.
D. 1.5 in.
The required diameter of the circle is given as 15 in. Option B is correct.
Given that,
The circumference of a circle is given 47.1 in, we have to determine the diameter of the circle.
Perimeter is the measure of the figure on its circumference.
Here,
As per the given condition,
First, write the formula for the circumference of the circle,
Circumference of the circle = πD
now substitute the value in the above equation,
47.1 = 3.14 D
D = 47.1/3.14
D = 15 in
Thus, the required diameter of the circle is given as 15 in. Option B is correct.
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there are 150 women who belong to a health club. The rest of the club members are men.3/5 of the members are men. How many members belong to the gym?
Answer:
3/5x 150
= 450/5
= 90
150+90
= 240 ans
Find two consecutive positive odd integers such that three times the sum of the largest number plus 22 is equal to the product of both numbers.
Answer:
Step-by-step explanation:
Let's say your consecutive numbers are A and B with A+2=B. Using the information we have been given, we can get the linear equation; AB=3B+22. A=B-2, so we can replace A with B-2 to get (B-2)(B)=3(B+22). Multiplying this out, we get B^2-2B=3B+66. Simplifying, we get B^2-5B-66=0. This is a quadratic equation. Using the quadratic formula, we get B=11,-6. B has to be positive, so B=11. A+2=11, so A=9
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation of the line in the slope intercept form is y = (-1/2)x + 60
From the given graph,
Choose two points
(0, 60) and (40, 40)
The slope of the line the change in y coordinates with respect to the change in x coordinate of the function
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the value in the equation
= [tex]\frac{40-60}{40-0}[/tex]
= -20/40
= -1/2
From the graph we can say that,
y intercept of the line = 60
The slope intercept form is
y = mx + b
where m is the slope of the line
b is the y intercept
y = (-1/2)x + 60
Hence, the equation of the line in the slope intercept form is y = (-1/2)x + 60
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What does 1.03 estimate to math
Answer:
provide context
Step-by-step explanation:
Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive. He wants each bag to have the same amount of pasta and sauce and wants to use all of the items.
The amount of pasta and sauce since he wants each bag to have the same amount is 16.
What is a factor?A factor simply means a number that can multiplied with another number which is also.a factor to get the original number.
In this case, Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive.
It should be noted that to get the number in each bag, it means that we have to find the highest common factor for both numbers. This will be:
Factors of 32 = 1, 2, 3, 4, 6, 8, 16 and 32
Factor of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Therefore, the answer is 16.
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How is this triangle congruent?
Answer:
triangle CBA is congruent to triangle CDA
The triangles are not congruent
8+ (-3) + (-8)
NEED HELP
Answer:
[tex]-3[/tex]
Step-by-step:
[tex]8+ (-3) + (-8)[/tex]
1 ) Combine like terms...
[tex]=5 - 8[/tex]
2 ) Solve...
[tex]= - 3[/tex]
Hope this helps! :)
What is the value of z? (The figure May not be drawn to scale.)
The value of z is given by (b) z = 63.
According to Angle Sum Property, the sum of interior angles of a triangle is 180 degree.
So for left hand triangle, interior angles are 31, 61 and x. So,
31 + 61 + x = 180
92 + x = 180
x = 180-92
x = 88
Now x and y are the linear angles so their sum is 180 degree too.
x + y = 180
88 + y = 180
y = 180-88 = 92
Again for right hand triangle the interior angles are 25, y, z. So again by Angle Sum Property,
25 + y + z = 180
25 + 92 + z = 180
117 + z = 180
z = 180-117 = 63
Hence the value of z is 63.
So the correct option is (b).
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Carly works 6 hours each day for 4 days a week
she earns £360 each week
How much does Carly earn each hour
Answer:
the answer is £15
Step-by-step explanation:
Carly works 6 hours for four days 6x4= 24
so she worked for 24 hours we know that she makes £360 per week.
so we divide 360 by 24 which gives us the total of
£15 per hour
The diameter of a quarter is 2.4 cm. You trace around the edge of the quarter on a sheet of paper. What is the area of the circle on the paper? Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
The area of the circle on the paper is 4.5 cm when traced around the edge of the quarter on a sheet of paper.
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
A = πr²
where 'r' is the radius of the circle
The diameter of a quarter is 2.4 cm. You trace around the edge of the quarter on a sheet of paper.
The area of the circle on the paper = πr²
Here r = (diameter of a quarter)/2 = 2.4/2 = 1.2 cm
The area of the circle on the paper = π(1.2)²
The area of the circle on the paper = π × 1.44
The area of the circle on the paper = 4.5238
Round the answer to the nearest tenth.
The area of the circle on the paper = 4.5 cm
Thus, the area of the circle on the paper is 4.5 cm
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Answer:its 4.5
Step-by-step explanation:
what are some integers whose product is negative?
The examples of some integers whose product is negative include:
-4 × 3 = -12
10 × (-2) = -20
What is an integer?An integer is a number that has no decimal or fractional part and can be negative or positive, including zero.
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
Integer examples include -5, 1, 5, 8, 97, and 3,043. Numbers that are not integers include: -1.43, 1 3/4, 3.14, and
In this case, the example has been given above. It should be noted that the product of a negative and positive number is a negative number.
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