The equation's directrix of [tex]y^{2}-6y-2x+19=0[/tex]. is 4.5 since this parabola's directrix's equation is x + a = 0.
what is equation ?
The statistic is said to be in a simplified sense when divided into its smallest equivalent fraction. What to do to determine the most basic form. Look for common factors in the denominators and numerators. A statement having two equal sides and then an equal sign in the midpoint is called an equation in mathematics. The conceptual model of any formula contains the degrees of all the variables given descending order. The typical form of a linear equation is an x + b = 0. This same general form of a mathematical expression with two variables is an x + b y + c = 0. (or something similar). Inequalities can be categorized either identities or dependent equations. An id holds true regardless of the value given to the variables.
given
Knowing the axis and vertex of a parabola allows one to determine the directrix of the curve.
The equation of the directrix of this parabola is x + a = 0 for an equation of the parabola in standard form [tex]y^{2} = 4ax[/tex], with focus at (a, 0) axis as the x-axis.
equation = [tex]y^{2}-6y-2x+19[/tex]=0
directrix x = h−p
(y−k)2 = 4p(x−h),p≠0
Directrix: x=4.5
The equation's directrix of [tex]y^{2}-6y-2x+19=0[/tex]. is 4.5 since this parabola's directrix's equation is x + a = 0.
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The complete question is:-
Find the directrix of this equation of y2-6y-2x+19=0
A soccer team made 2 goals out of 32 attempts in a game. What is the experimental probability that the team made a goal on any given shot? Write the probability as a decimal.
The experimental probability that the team made a goal on any given shot is 0.0625
How to determine the experimental probability that the team made a goal on any given shot?From the question, we have the following parameters that can be used in our computation:
A soccer team made 2 goals out of 32 attempts in a game
The experimental probability that the team made a goal on any given shot is calculated as:
P = 2/32
Evaluate the quotient
P = 0.0625
Hence, the probability is 0.0625
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A right triangle has legs of 33 inches and 44 inches
whose sides are changing. The short leg is increasing by 10 in/sec and the long leg is shrinking at 10 in/sec. What is the rate of change of the hypotenuse?
The rate of change of the hypotenuse is given as follows:
dh/dt = 2 in/sec.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
The hypotenuse is then given as follows:
h² = x² + y².
For this problem, the hypotenuse has the value given as follows:
h² = 33² + 44²
h = square root(33² + 44²)
h = 55.
Applying implicit differentiation, the rate of change of the hypotenuse is obtained by the equation as follows:
h dh/dt = x dx/dt + y dy/dt.
Replacing the values, the rate of change is calculated as follows:
55dh/dt = 33 x 10 - 44 x 10
55dh/dt = -110
dh/dt = -110/55
dh/dt = 2 in/sec.
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Select the phrase from the drop-down menu that
best completes the sentence.
Several values of a quadratic function are given
in the table.
X -5
y
-7
-2 -1 2
8 9
6
8 9
0 -40 -72 -91
There is a maximum between the two input values
>
Finish
Answer:
"of -1 and 2."
Step-by-step explanation:
The quadratic function has a maximum value between the two input values of -1 and 2, with a maximum output of 9.
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Answer:
It's the third choice.
Step-by-step explanation:
IF y varies inversely as x then y = k/x where k is a constant,
and k = xy
For the 3rd choice
-1 * -2/7 = 2/7
4 * 1/14 = 2/7 and
6 * 1/21 = 2/7
so, this is inverse variation.
Pat and Rich drove to the beach
last weekend. It took them twice as
long to get back as it did to drive
there. If they spent 9 hours traveling
to and from the beach, how long
did it take them to drive each way?
Step-by-step explanation:
Let's call the time it took Pat and Rich to drive to the beach "x".
The time it took them to drive back was twice as long, so it took 2x hours.
The total time spent traveling was x + 2x = 3x hours.
Since they spent 9 hours traveling, 3x = 9 hours.
So, x = 9 hours / 3 = 3 hours.
This means it took Pat and Rich 3 hours to drive to the beach and 2 * 3 = 6 hours to drive back.
Find the equation of the line passing through the point (8,−2) that is perpendicular to the line y=4/5x+4.
Answer: pls braiinliest :D
To find the equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4, we can use the concept of the slope of a line. The slope of a line perpendicular to another line has a negative reciprocal slope.
The slope of the line y = 4/5x + 4 is 4/5. The negative reciprocal of 4/5 is -5/4.
So, the slope of the line passing through (8, -2) and perpendicular to y = 4/5x + 4 is -5/4.
Next, we can use the point-slope form of a line to find the equation of the line:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the values, we get:
y - (-2) = -5/4 (x - 8)
Expanding and solving for y, we get:
y = -5/4x + 26/2
y = -5/4x + 13
The equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4 is y = -5/4x + 13.
Step-by-step explanation:
Can somebody help me with this? I need it answered fast please Also, I need to show work
The length of CE in the triangle is 20.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
From the given triangle ABC
BC=CD which are congruent sides
x-5=14
x=19
AB=DE
2x+3=6
2x=3
x=3/2
Now DE 2x+3=2(3/2)+3=6
CE=CD+DE
=14+6
=20
Hence, the length of CE in the triangle is 20.
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A large university accepts 60% of the students who apply. Of the students the university accepts, 45% actually enroll. If 20,000 students apply, how many actually enroll?
Please hurry will pay any amount
The number of students who got actually enrolled are, 5400
What are percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, a large university accepts 60% of the students who apply. Of the students the university accepts, 45% actually enroll, there are 20,000 students apply,
Since, the students whose application has been accepted = 20000 × 60%
= 12000
Now, the students who got admission = 12000 × 45%
= 5400
Hence, the number of students who got actually enrolled are, 5400
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D) What is the greatest common factor of 45 and 30?
Answer:15
Step-by-step explanation:
i did the math
Answer:
15
Step-by-step explanation:
15 x 2=30
15x3=45
Is the following true or false?
Every sample space S is a finite set.
The statement “Every sample space S is a finite set” is false because some sample spaces can be infinite, such as rolling a continuous random variable.
Explanation:The statement “Every sample space S is a finite set” is false. A sample space is the set of all possible outcomes of a random experiment. While some sample spaces may be finite, not all sample spaces are. There are situations where the sample space can be infinite, such as when rolling a continuous random variable like a dice.
For example, the sample space of rolling a fair six-sided die is finite, consisting of the numbers {1, 2, 3, 4, 5, 6}. However, the sample space of choosing a real number between 0 and 1 is infinite, as there are infinitely many possible outcomes between 0 and 1.
Therefore, it is incorrect to say that every sample space is a finite set.
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After kicking, one coach likes to play practice games with 6 players on each
team. She doesn’t like any team to have more or fewer than 6 players and
she doesn’t like anyone to be left off a team. What are the possible numbers
of players who must show up to practice so that the coach can make these
teams?
Answer:
The possible numbers of players are multiples of 6 (6, 12, 18, etc.).
Step-by-step explanation:
For the coach to be able to form teams of 6 players each, the total number of players must be divisible by 6. This means that if there are 6, 12, 18, 24, 30, etc. players, the coach can divide them evenly into teams of 6. Any other number of players would result in either having a team with more or fewer than 6 players, or leaving some players out. Hence, the possible numbers of players are multiples of 6.
The graph shows the time it takes Jacey to print T-shirts for her school’s math club.
The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.
What is a Proportional Quantities?If two variables of two quantities, x and y, are represented on a graph to show their relationship, they are proportional quantities if for every ratio of y to x, the value we get is the same, which means they have a constant of proportionality, k.
Using the points on the graph in the image attached below, the table can be completed as follows:
Part A:
Number of T-shirts (x): 1 2 3 4
Time in minutes (y): 5 10 15 20
Part B: Find the ratio of y to x for each of the points on the graph.
5/1 = 5
10/2 = 5
15/3 = 5
20/4 = 5
The table derived from the graph is:
Number of T-shirts (x): 1 2 3 4
Time in minutes (y): 5 10 15 20
B. The quantities are proportional.
The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.
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"Your question is incomplete, probably the complete question/missing part is:"
The missing information are in the attachment below.
This rectangle represents the base of a rectangular prism. The height of the rectangular prism is 56 m.
What is the volume of the rectangular prism?
Responses
A.212 m³
B.525 m³
C.5,600 m³
D.29,400 m³
A group of 8 students are painting a mural at the local library. Each student uses 1/4
of the paint in their bucket. How many total buckets of paint did the students use?
8 buckets each with 1 of 4 sections shaded.
Answer:
1/2 bucket
Step-by-step explanation:
Each of the 8 buckets is 1/4 full.
The total amount of paint at the beginning is 8 × 1/4 bucket = 2 buckets.
Each student uses 1/4 of his paint. Combined, they use 1/4 of the total amount of paint in the buckets.
1/4 × 2 buckets = 1/2 bucket
Answer: 1/2 bucket
How many solutions are there to the equation below?|x| = -4
A 0
B 2
C 4
D 1
Answer:
There are 0
Step-by-step explanation:
Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true
Answer:
A 0
Step-by-step explanation:
There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.
If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.
Match the mathematical expression with its translation.
1. x + y = 6
y divided by x
2. x + y
x minus y
3. xy
the product of two numbers
4.
x subtracted from y
5. y ÷ x
six less than a number is y
6. y = x - 6
six times a number equals y
7. x - y
the sum of two numbers is six
8. 6 x = y
the product of two numbers is six
9. xy = 6
the sum of x and y
10. y - x
x divided by y
The following mathematical expression matched with its translation:
1. x + y = 6 (the sum of two numbers is six)
2. x + y (the sum of x and y)
3. xy (the product of two numbers)
4. x ÷ y (x divided by y)
5. y ÷ x (y divided by x)
6. y = x - 6 (six less than a number is y)
7. x - y (x minus y)
8. 6 x = y (six times a number equals y)
9. xy = 6 (the product of two numbers is six)
10. y - x (x subtracted from y)
How to write mathematical expression?Mathematical expression can be translated as thus;
the sum of two numbers is six
Let the unknown numbers be x and y respectively
So,
x + y = 6
six less than a number is y
x - 6 = y
also written as
y = x - 6
six times a number equals y
6 × x = y
6x = y
also written as
y = 6x
Therefore, mathematical expressions are algebraic representation of mathematics in words.
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Mr. Lopez is looking to fill a part of a park with sand. The shape below represents the part of the park being covered in sand. How many square yards of the park will Mr. Lopez cover in sand?
Mr. Lopez cover in sand by 50 yd².
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
Mr. Lopez is looking to fill a part of a park with sand.
And, The shape below represents the part of the park being covered in sand.
Now, We will find the area of figure as;
The park is mix of two figure rectangle and triangle.
Hence, We get;
Area of rectangle = 5 × 8
= 40 yd²
And, Area of triangle = 1/2 × 4 × 5
= 10 yd²
Thus, The area of given figure is,
⇒ Area = 40 yd² + 10 yd²
⇒ Area = 50 yd²
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Carlos wants to finish a 7.5 mile trial
walking at a constant rate the distance that
Carlos has left
to finish the trial after h hours
walking is represented by the fuction 1h+2d=15
The domain of the function 5h + 2d = 15 is [0, 3].
What is domain and range of a function?
The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x).
The collection of numbers that the function assumes is known as its range. The values that the function outputs when we enter an x value are in this set.
5h + 2d = 15
2d = 15 - 5h
d = (15 - 5h)/2
For h = 0, d = 15/2 = 7.5
For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.
For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.
For h = 3, d = (15 - 15)/2 = 0 miles
The domain of the function is [0, 3].
Thus,
The domain is [0, 3].
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What is the value of x? - View the image attached.
Explanation:
The two horizontal sides are parallel. The side marked 34 is half as long as side x.
In other words, side x is twice as long as the side marked 34.
x = 2*34 = 68
For more information, search out "midsegment of a triangle".
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The set of pairs for which x and y vary inversely is given as follows:
{(-1, -2/7), (4, 1/14), (6, 1/21)}.
(third set).
What is a proportional relationship?A direct proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
For an inverse relation, the relation is modeled as follows:
y = k/x.
Meaning that when x increases, y decreases at a constant rate.
The constant is then obtained as follows:
k = yx.
Hence the third relation is then the relation for which x and y vary inversely, as:
k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.
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I need help with this question
The function which models the data as represented on the graph will be; [tex]f(x) = 0.8(1/2)^x[/tex].
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
The given graph is an exponential function and should take the form;
[tex]f (x) = a (b)^x[/tex]
Hence, using values from the graph;
For ( -1, 0.2 ) = a • b..........(i)
For (0, 0.8); 10.5 = a • b².........(ii)
=> x=0 and y= 0.8
So.
0.8=a(1/2)^0
0.8=a
Thus, the rule for the function is; y=0.8(1/2)^x
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Use the empirical rule. the mean speed of a sample of vehicles along a stretch of highway is 64 miles per hour, with a standard deviation of 4 miles per hour. estimate the percent of vehicles whose speeds are between 52 miles per hour and 70 miles per hour. (assume the data set has a bell-shaped distribution.)
The percentage of vehicles whose speeds are between 52 miles per hour and 70 miles per hour is 75%.
What is the empirical rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will fall within three standard deviations of the mean.
Given, The mean speed of a sample of vehicles along a stretch of highway is 64 miles per hour, with a standard deviation of 4 miles per hour.
[tex]\mu = 64[/tex] and [tex]\sigma = 4[/tex].
Now, 52 is 3 standard deviations away from the mean so 50% of the data falls into this category and 70 is 1.5 standard deviations away from the mean and 25% of the data falls into this category.
Therefore, 75% of the vehicles would fall into this category.
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AB formed by (-4, 7) and (-2, 6)
CD formed by (2, -2) and (-8, 3)
Is is parallel or perpendicular?
Line AB and CD are two parallel lines
What is the slope of a line:The slope of a line is defined as the change in y- the coordinate with respect to the x-coordinate and the formula is given by
Slope (m) = [ y₂ - y₁]/[x₂ - x₁]Note:
When two lines are parallel lines then the slope two line is equal When two lines are perpendicular lines then the product of the slope of two lines will be equal to '-1'
Here we have
AB formed by (-4, 7) and (-2, 6)
Slope of AB = (6 - 7)/(-2 + 4) = -1/2
CD formed by (2, -2) and (-8, 3)
Slope of CD = (3 + 2)/(-8 - 2) = 5/-10 = -1/2
Here Slope of AB = Slope of CD
As we know the slope of parallel lines is equal
Therefore,
Line AB and CD are two parallel lines
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It costs 9 dollars for 4 hot dogs.
What is the price of one hot dog?
The cost of 1 hot dog is $2.25
What is proportion?Proportion is a mathematical comparison between two numbers.
Given that, the cost of 4 hot dogs are $9, we need to find the cost of 1 hot dog,
Let the cost of 1 hot dog be x, therefore, setting the proportion,
4 / 9 = 1 / x
x = 9/4
x = 2.25
Hence, the cost of 1 hot dog is $2.25
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Consider the function graphed to the right.
The domain of the function is given as follows:
[-10,10].
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.The domain of a function is the set containing all the input values of the function.
Hence, on the graph, the domain of the function is composed by the values of x of the function, and is given as follows:
[-10,10]. (closed due to the closed circle).
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lydia has money in two savings accounts one rate is 8% and the other is 12% if she has $350 more in 12% account and the total interest is $336 how much is invested in each savings account
The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12% and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)
Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)
Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470
Now
y = 1470 + 350
y = $1820
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5. Jill drew 4 rectangles 3
triangles, 2 pentagons, and
3 trapezoids. How many
angles are on the
quadrilaterals she drew?
The angles on the quadrilaterals she drew are 47 in number.
What is Quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles
As there are four rectangles, The total number of angles in a rectangle are 4 × 4 = 16 angles.
The number of triangles is 3, the total number of angles is 3 × 3 = 9 angles.
Number of pentagons are 2, the total number of angles is 2 × 5 = 10 angles.
The number of trapezoids are 3, the total number of angles is 3 × 4 = 12 angles.
Total number of angles on the quadrilaterals she drew is 16 + 9 + 10 + 12 = 47 angles.
Hence, the angles on the quadrilaterals she drew 47.
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Even that the perimeter of a square varies directly with the side length what happens to the perimeter area of a square if the side length increases from s= 12 to s=36 inches?
Answer: The perimeter triples.
Step-by-step explanation:
Since there is a direct variation, if the side length triples, so does the perimeter.
Solve the inequality –3v – 2v > 35 for v.
A.
v < 7
B.
v > 7
C.
v < –7
D.
v > –7
Answer: c
Step-by-step explanation:
-3v - 2v > 35
combine like terms: -5v > 35
divde by the same term (isolate the variable): -5v/-5 , 35/-5
v < -7
h(9)=2x-3 evaluate the solution
The solution of the expression is, 15.
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.
We have to given that;
The expression is,
⇒ h (9) = 2x - 3
Now, Substitute x = 9, we get;
⇒ h (9) = 2 × 9 - 3
⇒ h (9) = 18 - 3
⇒ h (9) = 15
Thus, The solution of the expression is,
⇒ h (9) = 15
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