the vertex of the quadratic function is (4,-25).
What is a quadratic function?A quadratic function is a polynomial function with one or more variables where the highest exponent of the variable is 2. Due to the fact that the biggest degree term in a quadratic function is of second degree, it is sometimes referred to as the polynomial of degree two. It carries out algebraic functions.
examples of quadratic functions are:
f(x) = 2x2 + 4x - 5; Here a = 2, b = 4, c = -5f(x) = 3x2 - 9; Here a = 3, b = 0, c = -9f(x) = x2 - x; Here a = 1, b = -1, c = 0Given quadratic equation:f(x)=x²-8x-9
x-coordinate of vertex:
x=-b/2a
Putting the values, we get
x=-(-8)/2=4
Y-coordinate vertex:
y(4)=16-32-9=-16-9=-25
Vertex(4,-25)
Hence, the vertex of the function =(4,-25).
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Calculate the cost to treat one person who has TB if it costs R84 724 707 to treat 53 642 infected people. Give your answer correct to 2 decimal places.
The cost to treat one person who has TB is R1,579.82, rounded to 2 decimal places.
What is total cost?Total cost refers to the sum of all expenses incurred in producing a product or providing a service. It includes both the fixed costs (costs that remain constant regardless of the level of output) and variable costs (costs that vary with the level of output)
According to question:To calculate the cost to treat one person who has TB, we need to divide the total cost of treating all infected people by the number of infected people:
Cost to treat one person = Total cost of treatment / Number of infected people
Plugging in the given values, we get:
Cost to treat one person = R84,724,707 / 53,642
Cost to treat one person = R1,579.82
Therefore, the cost to treat one person who has TB is R1,579.82, rounded to 2 decimal places.
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what is the value of 6(2b-4) when b =3
Answer: 12
Step-by-step explanation:
Use BODMAS, so first solve the inside of the bracket:
2*3= 6
6-4= 2
Now we can multiply that by the number outside the bracket. Why?
Because a number outside a bracket means to multiply that number by everything in the bracket. So:
6 * 2 = 12
Answer: 12
Step-by-step explanation:
2 x 3 = 6
6 - 4 = 2
6 x 2 = 12
Question 7
Suppose the graph represents the scale drawing for a fence that Tara is building for a new city dog park. Each unit on the graph represents 12 yards. After studying the scale drawing, Tara decides to build a fence that encloses a smaller area. If Tara dilates rectangle ABCD by a scale factor of 0.75, and fencing costs $6.39 per yard, how much will she spend on fencing?
The total cost to fence the rectangular yard is given as follows:
$1,610.28.
How to obtain the perimeter of a triangle?The perimeter of a rectangle is the total distance around its outer boundary. To find the perimeter of a rectangle, you need to add up the lengths of all four sides.
If a rectangle has length l and width w, then its perimeter P is given by the equation presented as follows:
P = 2l + 2w
Considering the scale factor of 0.75, the distance represented by each unit on the graph is given as follows:
0.75 x 12 = 9 yards.
Hence the dimensions of the rectangle are given as follows:
Length of 8 x 9 = 72 yards.Width of 6 x 9 = 54 yards.The perimeter of the fence is then given as follows:
2 x (72 + 54) = 252 yards.
It costs $6.39 per yard, hence the total cost to fence the yard is given as follows:
252 x 6.39 = $1,610.28.
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The length of the longer leg of a 30 60 90 triangle is 6. The hyp is 9.
State the solution in Simple Root Form:
State the solution to the nearest tenth:
Step-by-step explanation:
there is something severely wrong with the problem definition.
when the Hypotenuse = 9, there is no 30-60-90 triangle with a leg = 6.
and when we are just focusing that this is a right-angled triangle with the Hypotenuse = 9, then 6 cannot be the longer leg.
it is also not clear what the solution is supposed to be. the 2nd leg ? the area ? the perimeter ? the height(s) ? ...
what ?
so, all I can do here is to show you why I said what I said :
30-60-90 triangle with Hypotenuse = 9
then the longer leg is opposite of the 60° angle and therefore sin(60)×9 = 7.794228634...
the shorter leg is opposite of the 30° angle and therefore sin(30)×9 = 0.5×9 = 4.5
a right-angled triangle with Hypotenuse = 9, one leg = 6 gives us per Pythagoras for the other leg
9² = 6² + leg²
81 = 36 + leg²
45 = leg²
leg = sqrt(45) = 6.708203932...
so, you see, as stated above, there is no leg with the length 6 in such a 30-60-90 triangle.
and in a more general right-angled triangle, if one leg = 6, then the other leg is actually longer.
therefore, there is everything wrong with the problem definition.
Find the measure of x.
Answer:
x = 25
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
71° is an exterior angle of the triangle , then
x + 46 = 71 ( subtract 46 from both sides )
x = 25
Three siblings, Peyton, Cameron, and Dakota, all ask their parents to borrow the family car for different events
around town. Since they cannot all borrow the car at the same time, the parents decide to use randomness to
decide who gets the car. They will roll a single, fair, six-sided number cube. Peyton gets the car if a 1 or 2 is
rolled. Cameron gets the car if a 3 or 4 is rolled, and Dakota gets the car if a 5 or 6 is rolled. Which of the
following is the probability distribution for who gets the car?
Well for each person, the probability is 1/3. This is because they all have 2 out of 6 possible outcomes.
These tables represent the relationships between x and y for two different sets of data.
Which statements correctly describe the relationships between x and y for each table?
Responses
Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.
Both data sets represent multiplicative relationships. In Table A, , y, is 3.5 times , x, , and in Table B, , y, is 9.2 times , x, .
Both tables represent additive relationships. In Table A, y is 2.5 more than x, and in Table B, y is 8.2 more than x.
Both tables represent additive relationships. In Table A, , y, is 2.5 more than , x, , and in Table B, , y, is 8.2 more than , x, .
Table A represents a multiplicative relationship because y is 3.5 times x, and Table B represents an additive relationship because y is 8.2 more than x.
Table A represents a multiplicative relationship because , y, is 3.5 times , x, , and Table B represents an additive relationship because , y, is 8.2 more than , x, .
Table A represents an additive relationship because y is 2.5 more than x, and Table B represents a multiplicative relationship because y is 9.2 times x.
Table A represents an additive relationship because , y, is 2.5 more than , x, , and Table B represents a multiplicative relationship because , y, is 9.2 times , x, .
Table A
x 1 2 3 4
y 3.5 7 10.5 14
Table B
x 1 2 3 4
y 9.2 10.2 11.2 12.2
Answer:
Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.
The correct statement is: Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.
Simultaneous Equations
y=x-2
y=3x+5
Hello and regards kiann09.
So the solution of the equation is:
x = - 7/2y = - 11/2Step-by-step explanation:y = x - 2
y = 3x + 5
We substitute the given value of y into the equation y = 3x + 5.
x - 2 = 3x + 5
We solve the equation for x.
x - 2 - 3x = 5
We move the variable to the left side and change its sign.
The sign of the variable must be changed because, in the process of "moving the variable", we are adding its opposite to both sides.
x - 2 - 3x = 5
Now we move the constant to the right hand side and change its sign.
x - 3x = 5 + 2
We group like terms.
-2x = 5 + 2 ⇒ We add the numbers ⇒ -2x + 7
We must divide both sides by -2.
x = - 7/2
We substitute the given value of x into the equation y = x - 2.
y = (-7/2)-2
We solve the equation for y. We write all the numerators above the common denominator.
y = -(7 + 4)/2
y = - 11/2
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Ken bought 3 3/4 pounds of apples at the farmers market Abby bought 2 1/8 pounds of apples how many pounds of apples did ken buy
Answer:Ken 3 3\4 pounds of apples
Step-by-step explanation:
Here are the first five terms of a geometric sequence.
√√5
10 20 √5
(a) Work out the next term of the sequence.
5√2
The 4th term of a different geometric sequence is
4
The 6th term of this sequence is
5√2
8
Given that the terms of this sequence are all positive,
(b) work out the first term of this sequence.
You must show all your working.
200
400 √5
Answer:
1/2
Step-by-step explanation:
20/√5 = 4√5
4√5 * (5√2 / 4√5) = 5√2
8 / 4 = 2
4 / (2^3) = 1/2
|1/2| = 1/2
The first term of this sequence is equal to 1/2
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is a and the term by which we multiply the previous term to get the next term is r
Then the sequence would look like
[tex]a, ar, ar^2, ar^3, \cdots[/tex]
Thus, the nth term of such sequence would be; [tex]T_n = ar^{n-1}[/tex](you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
We are given that The 4th term of a different geometric sequence is
4, The 6th term of this sequence is 5√2
20/√5 = 4√5
4√5 (5√2 / 4√5) = 5√2
8 / 4 = 2
Therefore,
4 / (2^3) = 1/2
|1/2| = 1/2
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Did it already but I don’t know if it is right.
Step-by-step explanation:
I'd say the association is linear, based on the first 3 options you chose
F(x)=5x+1 independent variable
Answer:
Step-by-step explanation:
bob had 2 apples and he ate 1 how many does he have now?
Answer: He has one left
Step-by-step explanation: 2-1=1
I need help anyone wants to help me with this to write it out :) thank you<3!!!
Answer:
Dip your finger in both whichever one is salty don't give to your plant
Step-by-step explanation:
Help with math problems
Answer:
13.) y=(x-4)^(2)+3
Step-by-step explanation:
Identify as a direct variation, inverse variation or neither. Y+x=10
Answer:
y=x10 is a direct variation, because everything you do to y will result in a similar change in x .
Use the following diagram for questions 21-24 in which G is the centroid of AABC, FC=35, AG=42, BF=57, and
DG=14.
Find AC
Find BG
Find GC
Find AE
G is the centroid of triangle ABC, AC = 85.5, BG = 38, GC = 23.33 (rounded to two decimal places), AE = 11.67 (rounded to two decimal places).
Describe Triangle?A triangle is a closed, two-dimensional shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry and is often used in various mathematical and scientific contexts.
The three sides of a triangle are usually named using lowercase letters a, b, and c, and the three angles are named using uppercase letters A, B, and C, with the opposite angles and sides having the same letter. The sum of the angles in a triangle is always 180 degrees, and this property is known as the Angle Sum Theorem.
Triangles can be classified based on their side lengths and angles. Based on the side lengths, triangles can be classified as:
Scalene triangle: A triangle in which all three sides have different lengths.
Isosceles triangle: A triangle in which two sides have the same length, and the third side has a different length.
Equilateral triangle: A triangle in which all three sides have the same length.
We can start by using the fact that G is the centroid of triangle ABC, which means that the medians from each vertex intersect at G. Therefore, we know that:
FC = 2/3 * EA (since FC is a median and EA is the corresponding segment of the opposite side)
AG = 2/3 * DC (since AG is a median and DC is the corresponding segment of the opposite side)
BF = 2/3 * AC (since BF is a median and AC is the corresponding segment of the opposite side)
We can use these relationships to find the lengths of AC, BG, GC, and AE:
AC = 3/2 * BF = 3/2 * 57 = 85.5
BG = 2/3 * AG = 2/3 * 2/3 * AC = 4/9 * 85.5 = 38
GC = 2/3 * FC = 2/3 * 35 = 23.33 (rounded to two decimal places)
AE = EA/2 = 2/3 * FC/2 = 1/3 * 35 = 11.67 (rounded to two decimal places)
Therefore, the answers are:
AC = 85.5
BG = 38
GC = 23.33 (rounded to two decimal places)
AE = 11.67 (rounded to two decimal places)
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A rocket is launched from the ground and follows a parabolic path. At the same time, a flare is launched from a height of 14 feet and follows a straight path. The following equations model a relationship between height of the object (y) and flight time (x)
Show your full work
Rocket: y = -x^2 + 8x
Flare: y = -x +14
Identify when the rocket and flare will collide first and their height at this time.
Time:
Height:
The maximum height οf the rοcket is 16 feet.
What is a System οf Equatiοns?A system οf equatiοns in algebra is made up οf twο οr mοre equatiοns that are sοlved tοgether. "A grοup οf equatiοns satisfied by the same set οf variables are called a system οf linear equatiοns. Finding the values οf the variables emplοyed in the system οf equatiοns is the first step tοwards sοlving it.
While maintaining the balance οf the equatiοns οn bοth sides, we cοmpute the values οf the unknοwn variables. Finding a variable whοse value makes the cοnditiοn οf all the given equatiοns true is the primary gοal οf sοlving an equatiοn system.
(x - 2)(x - 5) = 0
Sο x = 2 οr x = 5.
If x = 2, then frοm the equatiοn οf the flare, we have y = -2 + 14 = 12.
If x = 5, then frοm the equatiοn οf the flare, we have y = -5 + 14 = 9.
Sο the twο οbjects intersect at the pοints (2, 12) and (5, 9).
Tο find the maximum height οf the rοcket, we can use the fοrmula fοr the x-cοοrdinate οf the vertex οf a parabοla:
x = -b/2a
In this case, a = -1 and b = 8, sο we have:
x = -8/-2 = 4
Sο the rοcket reaches its maximum height at x = 4. Tο find the maximum height, we can substitute x = 4 intο the equatiοn fοr the rοcket:
[tex]y = -4^2 + 8(4) = 16[/tex]
Sο the maximum height οf the rοcket is 16 feet.
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Solve the equation √y+3=√y +√ 3
Step-by-step explanation:
so, it is
sqrt(y + 3) = sqrt(y) + sqrt(3)
first we square both sides :
y + 3 = y + 3 + 2×sqrt(y)×sqrt(3) =
= y + 3 + 2×sqrt(3y) =
= y + 3 + sqrt(4×3y) = y + 3 + sqrt(12y)
0 = sqrt(12y)
we square again :
0² = 12y
0/12 = 0 = y
Can you solve this question?
find dy/dx=?
We may conclude after answering the presented question that derivatives Therefore, the derivative of y = ln(cos(x)) with respect to x is: dy/dx = -tan(x)
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.
To find dy/dx when y = ln(cos(x)), we'll need to use the chain rule and the derivative of the natural logarithm.
[tex]dy/dx = (dy/du) * (du/dx)\\d/dx [ln(u)] = 1/u * du/dx\\dy/du = 1/u = 1/cos(x)\\dy/dx = (dy/du) * (du/dx) = (1/cos(x)) * (-sin(x)) = -tan(x)\\[/tex]
Therefore, the derivative of y = ln(cos(x)) with respect to x is:
dy/dx = -tan(x)
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A car salesman was able to sell a car for 12,500, earning a commission of 5%. How much was his commission.
Answer:
12,500 is 100%, or 1 in decimal terms. We calculate 5% by multiplying 12500 by 0.05.
This gives us a total of £625
Step-by-step explanation:
Brainliest pls
16 cm
14 cm
28 cm
What is the area of the trapazoid
Cuántos meses son 44 semanas
Answer:
alrededor de 10 meses
Step-by-step explanation:
please help ! QUICK no trolling
Answer:10.9
Step-by-step explanation:
using soh cah toa:
[tex]Sin40=\frac{b}{17}[/tex]
[tex]B=sin40 .17[/tex]
B=10.9
how many solutions does it have?
Y=x
Y=x-7
The number of solutions to the system of equation; y = x and y = x - 7 are;
There are no solution to the equation system
What is a solution to a system of equations?A solution is a set of the variable values in the equation system that make the system true at the same time.
The equations are;
y = x and y = x - 7
Whereby the right hand side of both equations are equated, we get;
x = x - 7
Subtracting x from both sides, we get;
x - x = x - 7 - x = -7
0 = -7
The above result is not true for all possible values of x, therefore, the system of equations has no solutions.Geometrically, the meaning of the equations is that the two lines representing the two equations do not intersect, and are parallel lines. This is shown by the slopes (the coefficient of x) of the two equations, which are the same (The slope is 1 in each equation)
The y-intercepts of the equations are however different (0 and -7), therefore, the two equations represent parallel lines with different y-intercepts
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im sorry for asking this i forgot to add this
A turtle and a snail are 300 feet apart when they start moving toward
each other. The turtle walks 5 feet per minute, and the snail crawls 1
foot per minute.
(How fast are the turtle and snail approaching each other?)
2 2/5 as an improper fraction in simplest form
Answer: 12/5
Step-by-step explanation:
Pls answer today and fast!!!! Use the tools below to make a triangle with angle measures or 60 degrees, 40 degrees, and 80 degrees.
An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. Angles are measured in degrees or radians and are typically denoted by symbol ∠ followed by the name of the vertex, like ∠ABC.
What is the Angle?The size of angle is determined by amount of rotation needed to bring one of rays or line segments into coincidence with others.
Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees).
Angles are fundamental to geometry and have many applications in physics, engineering, and other fields.
This is because the sum of the angles in a triangle must always be 180°, and 40° + 60° + 80° = 180°.
However, the angles do not satisfy the conditions of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, It is not possible to construct a triangle with angle measures of 40°, 60°, and 80°.
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Circle p has a radius of 8 inches
The area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
the angle of the sector = 70°
the radius = 8 ft
hence the area of the sector is calculated as follows:
(70°/360°) × 22/7 × 8 in × 8 in
we simplify by division and multiplication
1/36 × 22 × 64 in²
352 in²/9
39.1111 in²
Therefore, the area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.
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Find the area of one stretcher course of 18 concrete blocks if the blocks are 6 3/8 in long and 4 in high, and if the mortar joints are 1/8 in thick. (Hint: 18 blocks require 17 mortar joints.)
The area of one stretcher course of 18 concrete blocks is 467 1/2 square inches.
What is Area of stretcher course ?
To find the area of a stretcher course, you need to know the dimensions of the bricks or blocks, the number of bricks or blocks in the course, and the thickness of the mortar joints between them. The formula for the area of a stretcher course is:
Area of stretcher course = (Number of bricks or blocks) x (Length + Width) x Height
where Length is the length of each brick or block, Width is the width of each brick or block, and Height is the height of each brick or block.
According to the question :
To find the area of one stretcher course of 18 concrete blocks, we first need to calculate the total length and height of the course, taking into account the thickness of the mortar joints.
Length of the course = 18 blocks x 6 3/8 inches per block = 114 3/4 inches
Total width of the course = 17 mortar joints x 1/8 inch per joint = 2 1/8 inches
Height of the course = 4 inches
To calculate the area of the stretcher course, we need to multiply the length, width, and height of the course:
Area of stretcher course = Length x Width x Height
Area of stretcher course = (114 3/4 + 2 1/8) x 4
Area of stretcher course = (116 7/8) x 4
Area of stretcher course = 467 1/2 square inches
Therefore, the area of one stretcher course of 18 concrete blocks is 467 1/2 square inches.
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