The equation of the parabola that models the situation is given by:
(x - 1)² = -16(y - 5).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
(x - h)² = 4p(y - k).
The focus is located at point (h, k + p).
For this problem, to find the values of the parameters h and k, we have that:
The base is the vertex.The base is at (1,5).Hence:
h = 1, k = 5.
And:
(x - 1)² = 4p(y - 5).
For the focus, and subsequently to find parameter p, we have that:
The top is the focus.The top is at (1,1).Hence:
k + p = 1.
5 + p = 1
p = -4.
Then the equation of the parabola that models this situation is given by:
(x - 1)² = 4p(y - 5).
(x - 1)² = 4(-4)(y - 5).
(x - 1)² = -16(y - 5).
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a charity benefit is attended by 25 people and three gift certificates are given away as door prizes: one gift certificate is in the amount of $100, the second is worth $25 and the third is worth $10. assuming that no person receives more than one prize, how many different ways can the three gift certificates be awarded?
Number of ways that the three gift certificates can be awarded = 13800 ways
There are a total of 25 people attended the charity benefit. There are three gift certificates: one gift certificate is in the amount of $100, the second is worth $25 and the third is worth $10.
Assume that no person receives more than one prize.
One of the 25 people can get gift certificate of $100.
⇒ 25 ways for $100 gift certificate.
Then remaining 24 people are considered for further counting.
One of the 24 people can get gift certificate of $25.
⇒ 24 ways for $25 gift certificate.
Now there are 23 people remained.
One of the 23 people can get the $10 gift certificate.
⇒ 23 ways for $10 gift certificate.
Therefore, Number of ways that the three gift certificates can be awarded = 25 x 24 x 23 = 13800 ways.
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How can u determine whether a relation represented as an equation is a function
It can be determined that a relation represented as an equation is a function if and only if for each value on x-axis, there is a corresponding value on Y-axis.
which also signifies that for each value of x , there is a value of y which exists and is real.
A function is a mapping from one set to another such that nothing in the first set is mapped to more than one thing in the second set.
Or in simple words if there is no corresponding value of y for any x, then that is not a function.
For example,
[tex]x^{2} +y^{2}[/tex]=1
when the value of x is 0 , then value of y is 1 or -1, Thus, it will not be a function.
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use the given conditions to write an equation for the line. passing through (−9,2) and parallel to the line whose equation is
The given conditions to write an equation for the line passing through (−9,2) and parallel to the line whose equation is y = −3x+ 2.
What is an equation?There are many different methods to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically include one or more variables.
More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
[tex]$$We have the equation of a parallel line and a point which it passes through. To write the equation of the line in point-slope form, we will use the following formula:y−y1=m(x−x1)We know that the slope of parallel lines are same and we are given the equation for parallel line, y=−3x+2$$[/tex]
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researchers are investigating whether taking aspirin regularly reduces the risk of heart attacks. four hundred men participate in the study. the men are divided randomly into two groups: one group takes aspirin pills, and the other group takes placebo pills (a pill with no aspirin in it). the men each take one pill a day, and they do not know which group they are in. at the end of the study, researchers will count the number of men in each group who have had heart attacks. identify the explanatory and response variables in this situation.
Explanatory variable: The type of pill the men took each day.
Response variable: Whether a subject had a heart attack.
We have been given that :
Participated candidates are 400
Men are divided randomly so we find out explanatory and response variable.
The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.
Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.
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please help me with this Qestion
Answer: 5.5 inches
Step-by-step explanation:
Using the formula for the area of a square, we can plug the known values in and solve.
a = x²
30 = x²
[tex]\sqrt{30 } =\sqrt{x^2}[/tex]
[tex]\sqrt{30 }[/tex] = x
5.477 ≈ x
Now, we will round to the nearest tenth.
5.477 ≈ 5.5 inches
writing and graphing linear equations glass art
The graph of Linear Equation is always a straight line .
the scores on a statistics test had a mean of 81 and a standard deviation of 9. one student was absent on the test day, and his score wasn’t included in the calculation. if his score of 84 was added to the distribution of scores, what would happen to the mean and standard deviation?
Considering the concepts of the mean and the standard deviation, we have that:
The mean would increase.The standard deviation would remain constant.What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.When the measure of 84 is added, we have that:
A measure greater than the mean is added, hence the mean would increase.The difference squared between 84 and the mean of 81 is of 9, which is the same as the standard deviation, which would remain constant.More can be learned about the mean and the standard deviation of a data-set at https://brainly.com/question/26941429
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A skin on skin 63 photos in a minute if it’s skins photos at a consistent rate it can scan bring photos in 21 minutes
When it skins photos at a consistent rate, the number of photos in 21 minutes will be 1323 photos.
How to calculate the value?From the information, it should be noted that the skin on skin 63 photos in a minute.
Therefore, the number of photos that can be skinned at a particular minutes will be illustrated as:
p = 63m
where p = number of photos
m = number of minutes
Therefore, it should be noted that using p = 63m. The appropriate number of photos will be:
p = 63m
p = 63 × 21
p = 1323 photos
Therefore, when it skins photos at a consistent rate, the number of photos in 21 minutes will be 1323 photos.
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delroy is going to a dog adoption day at his local animal shelter. he wants to make 4 batches of dog biscuits for the dogs. it takes 1 3of a cup of margarine to make a batch. how many cups of margarine will he need?
4/3 cups of margarine will he need to make 4 batches of dog biscuits.
What is a fraction in math?A fraction is a piece of the entire. The number is shown as a quotient in mathematics, in which the numerator and denominator are split. Both are integers in a straightforward fraction. The numerator, as well as the denominator of a complex fraction, as well as the denominator of a complex portion, is a fraction.
What is a whole number in math?Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of corresponding positive numbers, which are additive, are the negative numbers. The blackboard bold math b Z or boldface Z is a common way to represent the set of integers in mathematical terminology.
According to the given information:There are four batches of dog biscuits.
Making a batch requires 1/3 cup of margarine.
As we can see that for 1 batch of dog biscuits required 1/3 cup of margarine.
So to make 4 batches of dog biscuits:
= (1/3)*4
= 4/3
4/3 cups of margarine will he need to make 4 batches of dog biscuits.
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At a grocery store, a customer pays a total of $9.70 for 1.8 pounds of potato salad and 1.4pounds of coleslaw. another customer pays a total of $6.55 for 1 pound of potato salad and 1.2pounds of coleslaw. how much do 2 pounds of potato salad and 2 pounds of coleslaw cost?
which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)?vertical translationhorizontal translationreflection over the x-axisreflection over the y-axis
The type of transformation that preserves the symmetry is Vertical translation.
For instance, a parabola is still symmetric about the y-axis if you move it up. It loses its symmetry if you move it to the left or right. Reflection keeps both even and odd functions symmetrical.
What is the difference between even and odd function ?The symmetry of a function is described using the terms even and odd. On a graph, an even function is symmetric about the y-axis. An odd function has symmetric behavior around a graph's origin [tex](0, 0)[/tex]. This means that if you rotate an odd function 180 degrees around the origin, the function you started with will still exist.
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Which quadratic inequality does the graph below represent?
Oy≤2x²-8x+3
O y≥ 2x² +8x+3
Oy≤2x²-8x-3
2 3 4 5 6 x
Answer:
A. y≤2x²-8x+3
Step-by-step explanation:
If you graph the function y≤2x²-8x+3, you would see that these both match.
The inequality y ≤ 2x² - 8x + 3 represents the given graph.
What is Inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Here, The y-intercept is 3, not -3, so answer C is eliminated
Choose a point that is clearly in the shaded area or one that is clearly in the unshaded region
Here, I choose the point (0, 0) and substituted these values in the equation and since 0 < 3,
Option A is the correct answer
Thus, the inequality y ≤ 2x² - 8x + 3 represents the given graph.
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An angle measures 84.2° less than the measure of its supplementary angle. What is the measure of each angle?
The measure of the supplementary angles are 48° and 132°.
Let the measure angle be x.
Its supplementary angle will be x + 84
We know that the sum of supplementary angles is 180°.
So, we get the equation as:
x + x + 84 = 180
Combining the like terms, we get that:
2 x + 84 = 180
Subtract 84 from both sides, we get that:
2 x = 180 - 84
2 x = 96
Divide both sides by 2, we get that:
x = 96 / 2
x = 48°
x + 84 = 48+ 84 = 132°
Therefore, we get that, the measure of the supplementary angles are 48° and 132°.
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I need help asap!!!!
Answer:
Step-by-step explanation:
You multiply the weight per gallon by the number of gallons, which is 3205.
So, 8.34 x 3205
A family is polled to see the mean of the number of hours per day the television set is on. The results, starting with Sunday, are 5, 2, 1, 2, 1, 2, and 6 hours. What is the average number of hours the family had the television set on to the nearest whole number?
The average number of hours the family had the television set on is 3 hours.
What is the average number of hours?The average of a set of numbers is calculated by adding the numbers together and dividing it by the total number. Average is also known as mean. Average is a measure of central tendency. Other measures of central tendency are mode and median.
Average = sum of the numbers / total number
Average = (5 + 2 + 1 + 2 + 1 + 2 + 6) / 7 =
19 / 7 = 2.714 hours
To round off a number to the nearest whole number, if the tenth digit is equal to 5 or greater than five, add one to the units digit. If this is not the case, the unit digit remain unchanged. In both cases, the tenth digit is replaced with o.
Because the tenth digit in 2.714 is greater than 5, the number becomes 3 hours.
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inspection of a random sample of 25 aircraft showed that 17 needed repairs to fix a wiring problem that might compromise safety. (a) how large a sample would be needed to estimate the true proportion of jets with the wiring problem, with 90 percent confidence and an error of ± 5 percent?
The random sample proportion.
Probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range.
at 90% confidence interval: The Central 90% of any normal distribution is: Z_(α/2) = 1.960
Error = E = ±5% = ±0.05
Applying the normal Probability distribution
= 0.70 ≤ P≤ 0.77(this means that we are 90% confident that the true proportion of jet with wiring problem fall with 0.70 and 0.77, hence there is no need for the airline to conduct further sampling, rather, they should just inspect all the planes)
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One of the main financial services that is provided by a bank involves offering accounts where people can safely store their money for a period of time, all the while earning interest and being protected by insurance. What is this common financial service called? A. payment services B. savings C. loans D. financial planning
Banks are known to carry out different functions. The common financial service called savings.
Financial services is known to be a very wide term that comprises of all of the activities such as banking, investing, and insurance.
Financial services by banks includes savings, investment, etc. Savings is thee process whereby bank helps to keep the money of its customers. It is known to be the most common services offered by banks.
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Hugo grapes triangle PQR and (Rt*T<3,1>)(truabgle PQR), where the equation of the line t is y=2, made exactly one error. Explain Hugo’s error
The Hugo's error is that , he did the translation incorrectly. He should have translated triangle by 3 unit right and then 1 unit up.
What is a triangle?In geometry, a triangle is defined as the shape which has three sides and also has three angles. We can say that a triangle is a type of polygon with three sides and three vertex. Triangle follows angle sum theorem.
Triangle Angle-Sum TheoremAccording to triangle Angle Sum theorem, the measurement of the sum of all interior angles of a triangle is always equals to 180°. That means, For a given triangle say ΔABC if ∠A, ∠B and ∠C are the interior angles then their sum i.e. ∠A + ∠B + ∠C = 180°.
Some important formula of triangles:
Area of triangle = 1/2 . base .heightPerimeter of triangle = sum of side lengthsNumber of vertices = 3Number of edges = 3In the question given,
the equation of line is y=2
The Hugo's error is that , he did the translation incorrectly. He should have translated triangle by 3 unit right and then 1 unit up.
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The complete question is :
Hugo grapes triangle PQR and (Rt*T<3,1>)(Δ PQR), where the equation of the line t is y=2, made exactly one error. Explain Hugo’s error.
work out the surface area of the prism
The surface area of the prism is 200 cm².
The surface area of the prism is given by the formula:
Surface area (S) = 2 B + p h
where B is the area of base of prism
p = perimeter of base
h = height of the prism.
Perimeter = 2(5 + 3) cm
p = 16 cm
B = 5 cm × 4 cm = 20 cm²
h = 10 cm
Substituting it in the formula, we get that:
S = 2 B + p h
S = 2 (20) + (16) (10)
S = 40 + 160
S = 200 cm²
Therefore, we get that, the surface area of the prism is 200 cm².
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If segment RS has endpoint R(5,1) and midpoint M(1,4), what will be point S?
Answer:
S(-3,7)
Step-by-step explanation:
Rise/Run
M(1,4) R(5,1)
1+run=5 4+rise=1
run=4 rise= -3
1-4= -3 4+3=7
-20=4x-6x
solve equation
Answer:
X=10
Step-by-step explanation:
-20=4x-6x
4x-6x=-20
[tex]\frac{-2x}{-2} =\frac{-20}{-2}[/tex]
X=10
Answer:
x = 10
Step-by-step explanation:
STEPS FOR SOLVING LINEAR EQUATION
−20=4x−6x
Combine 4x and −6x to get −2x.
−20=−2x
Swap sides so that all variable terms are on the left hand side.
−2x=−20
Divide both sides by −2.
x=
−2
−20
Divide −20 by −2 to get 10.
x=10
HELP PLEASE I DON'T UNDERSTAND :[
Answer: the first option i believe
Step-by-step explanation:
Hello I will AWard Brainlist !!! Help its A Math Question Please Help I will AWard Brainlist thanls so much !!!
The lengths 9, 9 / 2 and 9√3 are not part of a 30 - 60 - 90 right triangles. (Correct choice: A)
What set of measures are associated with a 30 - 60 - 90 right triangles?
Herein we must find what set of lengths are part of a 30 - 60 - 90 right triangle. In accordance with the Euclidean geometry, there are the following relationships for the sides of the 30 - 60 - 90 right triangle:
The longest leg is √3 times the length of the shortest leg.The hypotenuse is 2 times the length of the shortest leg.The hypotenuse is 2√3 / 3 times the length of the longest leg.Now we proceed to check if each set of sides belongs to a 30 - 60 - 90 right triangle:
Case 1
The length of the shortest leg of the triangle is 9 / 2, then the lengths of the longest leg and the hypotenuse are 9√3 / 2 and 9, respectively. (False)
Case 2
The length of the shortest leg of the triangle is 4, then the lengths of the longest leg and the hypotenuse are 4√3 and 8, respectively. (True)
Case 3
The length of the shortest leg of the triangle is 7, then the lengths of the longest leg and the hypotenuse are 7√3 and 14, respectively. (True)
Case 4
The length of the shortest leg of the triangle is 5 / 3, then the lengths of the longest leg and the hypotenuse are 5√3 / 3 and 10 / 3, respectively. (True)
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Mariana is younger than yaritza. their ages are consecutive odd integers. find mariana's age if the sum of mariana's age and 5 times yaritza's age is 100.
Translating the given word problem into a set of linear equations, Mariana's age is 15 years old.
Translate the given word problem into algebraic equations.
Let x be Mariana's age
Let y be Yaritza's age
Mariana is younger than Yaritza, their ages are consecutive odd integers.
Since the difference of consecutive odd integers is 2, then:
y = x + 2 ....... (1)
Sum of Mariana's age and 5 times Yaritza's age is 100.
x + 5y = 100 ..... (2)
Substitute equation (1) to equation (2)
x + 5y = 100
x + 5(x+2) = 100
6x + 10 = 100
6x = 90
x = 15
Thus, Mariana's age is 15 years old.
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Answer:
15
Step-by-step explanation:
i just got it right on delta
$600 son repartidos entre 3 amigos en la razón (2w + 3) : (w + 2) : (3w + 4), en donde w es un número positivo.
a) Si la menor parte es $125, forma una ecuación en términos de w y resuélvelo.
b) Luego, expresa la razón en la forma más simple.
c) Los 3 amigos deciden donar $50 cada uno a una caridad. Determina la razón de sus partes luego de la donación
The equation will be (2w ,+ 3) + (w + 2) + (3w + 4) = 600
The ratio in lowest term will be 2:1:3
When they donate $50, the ratio will be 1:4.
How to calculate the value?a. The equation based on the information will be:
(2w + 3) + (w + 2) + (3w + 4) = 600
6w + 9 = 600
6w = 600 - 9
6w = 591
Divide
w = 591/6
w = 98.5
b. Therefore, (2w + 3) = 2×98.5 + 3 = 200
(w + 2) = 98.5 + 2 = 100.5
(3w + 4) = 3(98.5) + 4 = 299.5
The ratio in lowest term will be 2:1:3.
c. When they donate $50, the ratio will be:
= (50 × 3)/600
= 150/600
= 1:4
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an equilateral triangle has three congruent sides that measure 1.5 inches on each side. what is the perimeter of the triangle?
The perimeter of the triangle is 4.5inches.
Equilateral Triangle : can be defined as a triangle having all three sides equal.
Perimeter of triangle is defined as the sum of the lengths of the three side.
Perimeter of triangle is denoted by 3x(side).
Given that the side of the triangle is 1.5 inches
Perimeter = 3x(1.5)
Perimeter=4.5 inches
Therefore , The Perimeter of the triangle is 4.5 inches .
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An electrician charges $24 per hour and $36 for each hour of overtime. For a job, the electrician works 8 regular hours and overtime hours. He also charges $202 for materials. The total amount of the bill for the job is $538. How many overtime hours did the electrician work?
Fill in the blanks to create an equation that represents the situation.
Blanks-
24( )+ x+202=538
Answer:
hindi kasi ka nag aaral hhahhaha
Error Analysis A worker in a silver mine descends 78 feet. Use an integer to represent the change in the worker's position.
An integer to represent the change in the worker position is -78
If the worker is descending, he is going down.The change in his position could be marked on a graph by translating the original point down by 60 units. Integers are a set of numbers that include the positive whole numbers (1,2,3,4,5,....), their opposites (-1,-2,-3,-4,-5,...) are zero. This number line shows the integers from -5 to 5 .You can use integers to help represent many real - world situations, such as:Increase and decreases in temperature.Profits and losses of moneyLocations above and below sea level.Hence, An integer to represent the change in the worker position is -78
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π x 910(10)
PLEAS ENEMOPOEJDHE HELP
Answer:
The correct is the 9100πx
Im doing geometry, I forgot how to do this.
Answer:
12
Step-by-step explanation:
You have a right triangle, so use the Pythagorean theorem.
a² + b² = c²
5² + b² = 13²
25 + b² = 169
b² = 144
b = 12