The altitude of the original pyramid is about 75.11 units
Given that,
Let h stand in for the original pyramid's height. The cut-off top then stands at a height of (h -22). The square of the scale factor for height is the scale factor for area, therefore we get :
Altitude of Pyramid means The slant height of a regular pyramid is its lateral face's height. Slant height in a non-rectangular pyramid is not specified. When determining the height (or altitude) of a regular, right pyramid, the vertex (the top) is used as the point perpendicular to the base. The base will intersect at this position.
(Height ratio)^2 = 1/2
((h -22)/h) ^ 2 = 1/2
(h-22) / h = 1/[tex]\sqrt{2}[/tex]
h-22 = h /[tex]\sqrt{2}[/tex]
h = 75.11 units
Consequently, the original pyramid's altitude is around 75.11 units.
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Given the following list of axioms, draw a model to properly represent the information.
a. there exists five points
b. there exists two lines
c. each line consists of at least two points
d. each line contains only these five points.
The model which properly represent the information in given axioms is Cross geometry (+).
In the given question we have following information,
total number of points in model is 5total number of lines in model is 2each line consists atleast 2 pointseach line contains only these five pointsby using the above axioms we draw a geometry of Cross sign Geometry as seen above .
We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .
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a student was asked to find the equation of the tangent plane to the surface at the point . the student's answer was (a) at a glance, how do you know this is wrong. what mistakes did the student make? select all that apply. a. the answer is not a linear function. b. the (x - 5) and (y - 4) should be x and y. c. the partial derivatives were not evaluated a the point. d. the -131 should not be in the answer. e. all of the above (b) find the correct equation for the tangent plane.
The answer is not a linear function, and the evaluation of the partial derivatives was done to a point. Thus, options (a) and (c) are correct. The correct equation for the tangent plane is z = 3x - 108y - z + 241 = 0.
In a given point (x₀, y, z₀) the equation of the tangent plane to a surface given by the function S = f(x, y)can be obtained by
z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀) ... (i)
where f ₓ (x₀, y₀, z₀) and fᵧ (x₀, y₀, z₀) (y - y₀) are the partial derivatives of f(x, y) with respect to x and y respectively. These two derivatives are evaluated at the point (x₀, y₀, z₀) .
Thus, we need to find two missing inputs, the z₀ coordinate and the two partial derivatives, in our problem in order to use equation (i).
In the case of z₀, evaluation of the given function gives us z = -80.
The partial derivatives are thus-
δf(x,y) / δx = fₓ (x, y) = 3x²
fₓ (x₀, y₀) = fₓ (1, 3) = 3
δf(x,y)/δxy= fᵧ (x, y) = -4y³
fᵧ (x₀, y₀) = fᵧ (1, 3) = -108
Now, arranging these values in equation (i) we obtain:
z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀)
z +80 = 3x² (x -1) - 4y³ (y - 3)
z = -80 +3x² (x -1) - 4y³ (y - 3)
Now, we will substitute the values of the partial derivatives at the given point:
z = -80 + 3x² (x -1) - 4y³ (y - 3)
z = 3x² (x -1) - 108 (y - 3)
z = 241 + 3x -108y
i.e., 3x - 108y - z + 241
Thus, the correct equation is 3x - 108y - z + 241.
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The complete question is-
A student was asked to find the equation of the tangent plane to the surface z = x³−y⁴ at the point (x, y) = (1, 3). The student's answer was z = −80 + 3x²(x−1)−(4y³)(y−3).
(a) At a glance, how do you know this is wrong? What mistakes did the student make? Select all that apply. A. The (x - 1) and (y - 3) should be x and y. B. The -80 should not be in the answer. C. The partial derivatives were not evaluated at this point. D. The correct answer is not a linear function. E. All of the above.
(b) What is the correct equation for the tangent plane? z=
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A floral shop earns an average yearly revenue of $195,280. Which compound inequality correctly shows the amount of money, m, the floral shop needs each month to pay for rent if the monthly budget for rent is between 10% and 15%? $375.54 sm≤ $563.31 $751.08 sm≤ $1,126.62 $1,627.33 sm ≤ $2,441.00 $1,502.15 sm s $2,523.23
The monthly budget for rent is $1,627.33 ≤ m ≤ $2,441.00
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let m represent the monthly rent of the shop.
The average yearly revenue is $195,280. Hence:
Monthly revenue = $195,280 / 12 = $16273.33
If the monthly budget for rent is 10%, hence:
m = 10% of $16273.33 = 0.1 * $16273.33 = $1627.33
If the monthly budget for rent is 15%, hence:
m = 15% of $16273.33 = 0.15 * $16273.33 = $2441.00
$1,627.33 ≤ m ≤ $2,441.00
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3.472 divided by ____=0.112 free 25 points!!
When the divisor is missing, you divide the dividend (3.472) by the quotient (0.112)
So, we will do 3.472 divided by 0.112
3.472/0.112 = 31
Another method is multiplication. Multiplication is the opposite of division. We'd multiply 0.112 by 31.
0.112 x 31 = 3.472
In conclusion,
3.472/31 = 0.122
If you need extra help, use this video as a reference
https://youtu.be/9ui8Yh0bwCI?t=83
Answer: 3.472/31 = 0.122
Step-by-step explanation: I hope this helps:)
The area of the rectangle ABCD is 28[tex]cm^{2}[/tex]
a) What is the length of side AB in terms of x?
length of AB = (Answer here) (1)
b) If the area of rectangle ABCD is 28[tex]cm^{2}[/tex], we can show that [tex]x^{2}[/tex] + ax = b where a and b are integer values.
Work out the values of a and b.
a = (Answer here) (1) b = (Answer here) (1)
Answer:
see explanation
Step-by-step explanation:
(a)
AB = 4 + x
(b)
the area (A) of rectangle ABCD is calculated as
A = length × breadth
= AB × AD
= (4 + x)(6 + x) ← expand using FOIL
= 24 + 10x + x²
given A = 28 , then
x² + 10x + 24 = 28 ( subtract 24 from both sides )
x² + 10x = 4 ← in the form x² + ax = b
with a = 10 and b = 4
the recursive formula for the height above the ground on the nth step of the stairs show is an=an-1+4 with a1=7 what explicit formula finds the height above the ground of the nth step?
The explicit formula is a_n = 3+4n
From the question, we have
a1 = 7
We know that,
a_n = a_1 +(n-1)d
a_n = 7 +(n-1)4
a_n = 7+4n-4
a_n = 3+4n
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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Ty bought three and four-sixths pounds of coffee. He gave five-sixths of a pound to his grandma. Estimate how much coffee Ty has left.
5 pounds
four and one-half pounds
3 pounds
two and one-half pounds
Ty has 2 5/6 pounds of coffee left after giving 5/6 pounds of coffee to his grandma
What is fraction?Fraction is a numerical quantity that is not a whole number
From the question,
Ty bought 3 4/6 pounds of coffee
converting 3 4/6 to improper fraction
we have 22/6
Ty gave his friend 5/6 pound of coffee to his grandma
To estimate how much coffee Ty has left
We substract Coffee given to his grandma from Coffee bought
That is,
22/6 - 5/6
= 17/6
= 2 5/6 pounds of coffee left
Ty has 2 5/6 pounds of toffee left. He gave 5/6 of what he bought to his grandma.
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Today, I want you to challenge yourself. Don't let word problems intimidate you. In this task you are not solving but rather setting up equations. I know you have the
ability to do this. Here we go!
19
A store sells two brands of headphones: high definition (HD) and basic. It buys x HD headphones at z dollars each, and y basic headphones at w dollars each.
In a-c, write an equation whose solution is the given quantity. Solve Each Equation and set them up.
a) The number of basic headphones the store can purchase if it spends a total of $10,000 on headphones and buys 110 HD headphones for $70 each.
b)
The price the store pays for HD headphones if it spends a total of $2,000 on headphones and buys 55 basic headphones for $20 each.
c) The price the store pays for HD headphones if it spends a total of $800 on headphones and buys eight basic headphones for $80 each.
d) Please give me the actual cost of the headphones and an explanation with a-c
The solution to these are in form of equation as follows.
What is equation?
In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
x= number of HD headphones y= number of basic headphones
z = price of HD headphones. w = price of basic headphones
a)
110 (70) + y*w = 10,000
7,700+ y*w = 10,000
y*w = 2,300
y = 2,300/w
b)
x*z+ 55(20) = 2000
x*z = 2000 -1100
x*z = 900
z = 900/x
c)
x*z+y*w = 800
x*z+8(80) = 800
x*z+640=800
X*z=160
Hence the values to the equation are as follows.
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simply the following ratio:-
2/3:1/6:5/2
Step-by-step explanation:
ratios are special fractions and follow therefore all the fraction rules.
e.g. they follow the rule that for transformations the same multiplications or divisions have to happen for the denominator and the numerator when bringing them to the same denominator.
and they follow the same division and multiplication rules.
2/3 : 1/6 : 5/2 = (2/3)×(2/2) : 1/6 : (5/2)×(3/3) =
4/6 : 1/6 : 15/6 = 4 : 1 : 15
(Help!)
#8 The tables represent some points on the graphs of lines m and n. Which system of equations is represented by lines m and n?
(A) −6x − y = 8 −3x + 2y = 9
(B)6x + y = −8 3x − 2y = 9
(C) 6x − y = −8 −3x − 2y = 9
(D) 6x − y = 8 3x + 2y = 9
#9 A produce company sells crates filled with a mixture of apples and oranges during the holiday season to grocery stores. Each crate contains a total of 72 pieces of fruit. Suppose that a crate has 8 more apples than oranges.
Which system of linear equations can be used to determine the number of pieces of each kind of fruit in the crate?
(A) a + o = 72 o = a + 8
(B) 8a + o = 72 a + o = 8
(C) a + o = 72 a = o + 8
(D) a + 8o = 72 a + o = 8
#10 The tables represent some points on the graphs of lines r and s. Which system of equations is represented by lines r and s?
(A) −4x + 3y = 12 2x − 5y = −10
(B) −4x − 3y = −12 −2x + 5y = 10
(C) 4x + 3y = −12 2x − 5y = 10
(D) 4x − 3y = −12 −2x − 5y = 10
The linear functions representing the systems of equations in each case are given as follows:
8. (D) 6x − y = 8 3x + 2y = 9
9. (C) a + o = 72 a = o + 8.
10. (C) 4x + 3y = −12 2x − 5y = 10.
What is a linear function?The slope-intercept representation of a linear function is presented by the rule as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.b is the y-intercept of the function, being the numeric value of the function when the input variable x assumes a value of 0.For the line m, we have that when x increases by 6, y increases by 36, hence the slope is:
m = 36/6 = 6.
Considering the positive slope of 6, at x = 0, the numeric value is 12 less than the numeric value at x = 2, hence the intercept is:
b = 4 - 2 x 6 = -8.
Hence the equation is:
y = 6x - 8.
6x - y - 8.
Thus option d is correct.
For item 9, we use the variables a and o. The total is of 72, hence:
a + o = 72.
Suppose that a crate has 8 more apples than oranges, hence:
a = o + 8.
Thus option c is correct.
For line r in item 10, when x increases by 3, y decays by 4, hence the slope is:
m = -4/3.
When x = 0, y = -4, hence the intercept is:
b = -4.
Thus the equation is:
y = -4x/3 - 4
3y = -4x - 4.
4x + 3y = -12.
Meaning that option c is correct.
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The volume of box A is 64 cubic inches. The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches. Can a baseball fit in box A?
Yes, a baseball fit in box A.
What is Volume?Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m³, cm³, in³, etc.
Volume is simply the amount of space a three-dimensional solid takes up. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.
Given:
The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches.
So, the maximum value of Circumference
2πr = 9.5
r= 9.5/ 2 x 3.14
r = 1.472 inch
So, Volume of ball = 4/3 πr³
Volume of ball = 4/3 x 3.14 x (1.472)³
Volume of ball = 13.36 inch³ < 64 inch³
Hence, it will fit inside the box.
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8 coins are simultaneously flipped. what is the probability that heads are showing on at most 2 of them?
The probability of favorable outcomes P(E) = 37/256
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Given,
8 coins are faced simultaneously .
total outcomes = 2 * 2 * 2* 2 * 2 * 2 * 2 * 2
= 2⁸
= 256
favorable outcomes = 6 heads + 7 heads + 8 heads
= ⁸C₆ + ⁸C₇ + ⁸C₈
= 28 + 8 + 1 = 37
the probability of favorable outcomes =
P(E) = 37/256
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Q8.
Solve the simultaneous equations
2x + 3y = 5p
y = 2x + p
where p is a constant.
Give your answers in terms of p in their simplest form.
Answer:
x = 1/4p
y = 3/2p
Step-by-step explanation:
2x + 3y =5p__________________equ 1
y = 2x + p____________________equ 2
sub equ 2 for y in equ 1
2x + 3(2x + p) = 5p_______________open brackets
8x = 2p______________________divide both sides by 8
x = 1/4p
sub 1/4p for x in equ 2
y = 2(1/4p) + p___________________open brackets
y = 3/2p
What is the inequality of the graph below?
The inequality of the graph represented in the figure is y ≥ 1/2x
How to determine the inequality of the graph?The graph represents the given parameter
On the graph, we have the following points
(x, y) = (0, 0) and (2, 1)
This can be re-expressed as
(x, y) = (2, 1)
The slope is then calculated as
Slope = y/x
This gives
Slope = 1/2
The equation is then calculated as
y = Slope * x
So, we have
y = 1/2x
On the graph, we can see that the upper part of the graph is shaded and the line is a thick line
This means that the inequality expression is ≥
So, we have
y ≥ 1/2x
Hence, the inequality of the graph is y ≥ 1/2x
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The equation 2x(x + 8) = 110 represents the area of a rectangle.
Solve the equation. What are the approximate dimensions of the rectangle? Express your answers as decimals rounded to the nearest tenth.
The rectangle has its dimensions to be 8.8 units by 12.4 units
How to determine the dimensions of the rectangle?From the question, the equation is given as
2x(x + 8) = 110
This equation represents the area of the rectangle
So, we have
2x(x + 8) = 110
Divide by 2
x(x + 8) = 55
Open the brackets
This gives
x² + 8x = 55
Rewrite as
x² + 8x - 55 = 0
Using a graphing calculator, we have the solutions to be
x = -12.4 and x = 4.4
The variable x cannot be negative
So, we have
x = 4.4
In 2x(x + 8) = 110, we have
Length = 2x
Width = x + 8
So, we have
Length = 2 x 4.4
Width = 4.4 + 8
Evaluate
Length = 8.8
Width = 12.4
Hence, the dimensions of the rectangle are 8.8 units by 12.4 units
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Which values of aand b make the following equation true?
(5x²y²){-4xªy³) =−20xªy°
O
a = 11, b = 7
O a = 11, b = 10
O a=28, b = 7
O a= 28, b = 10
The value a = 2 and b = 5 is makes the expression (5x²y²){-4xªy³) =−20xªyᵇ as true.
Expression:
An expression is set of numbers or variables combined using the operations +, -, * and /.
Given,
Here we have the expression (5x²y²){-4xªy³) =−20xªy°.
Now, we have to the value of a and b which make both equation as equal.
In order to get the value a and b, first, we have to solve the expression in the left hand side,
To solve this type of equation, the first step is to combine the like terms, then we get,
=> (5x²y²){-4xªy³)
=> (5 x -4) (x² xᵃ) (y² y³)
Now, we have to do the multiplication on it, then we get,
=> -20 xᵃ⁺² y²⁺³
=> -20xᵃ⁺²y⁵
Now, we have to equate both LHS and RHS, then we get,
=> -20xᵃ⁺²y⁵ = -20xᵃyᵇ
While we looking into the equation, we have identified that the value of a is 2 and the value of b is 5.
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The theater director recorded the number of seats occupied at past performances and the total revenue per
performance.
After plotting her results, the director noticed that the relationship between the two variables was fairly linear,
so she used the data to calculate the following least squares regression equation for predicting the total
revenue, in dollars, from the number of seats occupied.
= -325 + 143
What is the residual of a performance with a revenue of $700 and 70 seats occupied ?
The residual of a theatre performance with a revenue of $700 and 70 seats occupied is 45.
What is the residual of the performance?From the information illustrated, the theater director recorded the number of seats occupied at past performances and the total revenue per performance.
The equation is given as:
y = -325 + 14x
y = actual performance for 70 seats occupied
For x = 70
y = -325 + 14x
= 325 + 14(70)
= -325 + 980
= 655
Therefore, the residual will be:
= 700 - 655
= 45
The residual is 45.
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What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Equation of the line for the given graph in slope-intercept form is given by y = 5x -1.
As given in the question,
From the given graph,
Consider pair of two coordinates we have,
(x₁ , y₁) = (1, 4)
(x₂ , y₂) = (0,-1)
Equation of the line for the given graph in slope-intercept form is given by:
(y -y₁) / (x -x₁)= (y₂ -y₁) / (x₂ -x₁)
⇒ ( y - 4)/ (x -1) = (-1-4)/(0-1)
⇒(y-4)/(x-1) = 5
⇒y-4 = 5(x-1)
⇒y = 5x -5 +4
⇒ y= 5x -1
Therefore, equation of the line for the given graph in slope-intercept form is given by y = 5x -1.
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Solve the system of equations using substitution.
3x + 2y = 7
x = 3y + 6
The solution of the system of equation by substitution is x = 3 and y = -1.
How to solve system of equation by substitution?System of equation can be solved using different techniques such as substitution method, elimination method and graphical method.
Let's solve the system of equation by substitution method
Therefore,
3x + 2y = 7
x = 3y + 6
Substitute equation(ii) in equation(i)
3(3y + 6) + 2y = 7
9y + 18 + 2y = 7
9y + 2y + 18 = 7
11y = 7 - 18
11y = -11
y = -11 / 11
y = -1
Hence, let's find x
x = 3(-1) + 6
x = -3 + 6
x = 3
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A red-throated loon is a type of diving bird that dives for its food. One particular loon dives for 8 seconds to a depth of 12 feet under the surface of the water. A. Assume the loon dives at a constant rate. Write an equation that can be used to represent the elevation, y, of the loon after x seconds into the dive. B. If the loon is at a depth of 22 feet under the surface of the water, how long was it diving for? Show your work.
The equation representing the elevation of the loon and the time of the dive is 3x-2y = 0, and the Loon has been diving for 14.67 seconds.
The red throated loon dived down to a distance of 12 feet under the water in 8 seconds.
We can assume that the loon is diving at a constant rate.
The relation between the elevation wise of the loan after 1 second into the dive can be represented by the linear equation which has the slope,
Slope = 12/8
Slope = 3/2
Now as we have the slope of the equation we can write the equation by using the point slope form, with the point, (8,12)
(y - 12)/(x - 8) = 3/2
2y - 24 = 3x - 24
3x - 2y = 0
This is the equation that represent the elevation y of the loan after x seconds.
When the elevation of The Loon is 22 feet,
We can put y = 22,
3x = 2(22)
x = 14.67 seconds.
So, the loon has been diving for 14.67 seconds.
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a jar contains 4 red marbles numbered 1 to 4 and 8 blue marbles numbered 1 to 8. a marble is drawn at random from the jar. find the probability of the given event. write your answers as reduced fractions. (a) the marble is red your answer is : (b) the marble is odd-numbered your answer is : (c) the marble is red or odd-numbered your answer is : (d) the marble is blue and even-numbered your answer is :
each of ncustomers gives a hat to a hat-check person at a restaurant. the hat-check person gives the hats back to the customers in a random order. what is the expected number of customers that get back their own hat? derive your answer by using random variables and expected values of random variables.
The expected number of customers that get back their own hat is 1.
Define the term random variables?A random variable is called with an unspecified amount or a function that gives values to each of the results of an experiment. There are two types of random variables: discrete (having specified values) and continuous (value in a continuous range).Utilizing indicator random variables, we resolve this issue. For 1 ≤ i ≤ n,
Let .
Xi = I {Customer 'i' who gets his hat back itself}.
The number of clients that receive their own hats back should be the random variable X. We want to figure out E[X].
Clearly,
n
X = ∑ Xi
i=1
It is clear that 1/n represents the likelihood that customer 'I' will receive his own hat.
Due to the fundamental characteristics of indicator random variables, this means that E[Xi] = 1/n.
n
E[X] = E [ ∑ Xi ]
i=1
n
= ∑ 1/n
i=1
Put the limits.
E[X] = 1
As a result, 1 consumer is anticipated to have their own hats back.
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What’s the answer plss
Answer:
<ABD = 67.17
Step-by-step explanation:
Comment
This requires 2 steps.
Find <AFind <ABDFinding <A
<A is found by taking the inverse tangent of the ratio 8/19.
<A = tan-1*(8/19)
<A = 22.83 degrees. We'll round it later.
Finding <ABD
You have to use 2 facts here.
All triangle angles add up to 180 degrees.
You find the third angle by subtracting the other 2.
<A = 22.83 Found above
<ADB = 90 degrees Given
<ABD = ?
Equation
< A + <ADB + <ABD = 180
Solution
22,83 + 90 + <ABD = 180 Combine the left
112.83 + <ABD = 180 Subtract 112.83 from both sides.
112.83-112.83 +<ABD = 180 - 112.83 Combine
<ABD = 67.17
The answer to the nearest degree is 67.
help me please please please 33333
Expand using Pascal's triangle: (x + 1)4.
Answer:
[tex] {x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4x + 1[/tex]
Step-by-step explanation:
as shown in photo attached :")
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The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
The equation of the parabola
f(x) = [tex]7x^2[/tex]
The standard vertex form of a parabola is
y = [tex]a(x-h)^2[/tex] + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) = [tex]7x^2[/tex]
The value of a = 7
Substitute the values in the vertex form of a parabola
y = [tex]7(x-3)^2[/tex] + 5
Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
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The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3
The quadratic function is
f(x) = [tex]-3x^2[/tex] + 18x + 3
The general form of the quadratic function is
y = [tex]ax^2[/tex] + bx + c
If a < 0, the quadratic function has maximum value
Here the value of a = -3
Therefore the function has maximum value.
Maximum value will be at x = -b / 2a
= -18 / 2(-3)
= -18 / -6
= 3
The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a
Substitute the value in the equation
(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3
= (-36 - 324 / -12
= -360 / -12
= 30
Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3
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Find the equation of the vertical line that passes through point M(−2, 6)
The equation for the vertical line that goes through point M(−2, 6) is x = -2.
Answer:
The equation of a straight line is:
y = mx + b;
y, x are variables, m is the slope of the line and b is the y intercept.
The slope of a vertical is undefined. Since the line passes through the point M(−2, 6), hence the equation of the vertical line is:
x = -2
What are the terms of this algebraic equations 3+6ab+c? 3,6ab 6ab,c 3,6ab, and c
The terms of the algebraic equation 3+6ab+c are (d) 3, 6ab and c
How to determine the terms of the equation?The algebraic equation is given as
3 + 6ab + c
Consider an equation represented as
x + y
The terms of the equation are x and y
Also, for an equation represented as
x + y + z;
The terms are x, y and z
Using the above as a guide, the terms of 3 + 6ab + c are 3, 6ab and c
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adriel finds some dimes and quarters in his piggy bank. how much money (in dollars) does he have if he has 12 dimes and 10 quarters? how much money (in dollars) does he have if he has xx dimes and yy quarters?
Answer:
$3.70
Step-by-step explanation:
12 dimes, and dimes are ten cents each. So we will multiply 10*12=120. Which is $1.20.
10 quarters, and quarters are twenty-five cents each. So we will multiply 10*25=250. Which is $2.50
Now we take our two totals and add them together. 1.20+2.50=3.70.
So we have $3.70.
I hope this helps!!!
