y-values have constant first differences in a linear table,
y-values have constant second differences in quadratic table and
y-values have equal rations in exponential table.
To tell the difference between a linear, quadratic and exponential table we have to see the variation in y-values as the x-values increases by constant amount
Linear Function:
A function is said to be a Linear Function if it has either one or two variables without exponents
It is of the form: y = f(x) = px + q
It has one independent and one dependent variable.
The graph of a Linear function is a straight line.
Quadratic Function:
A function is said to be a Quadratic function is it of the form
f(x) = px^2 + qx + r
Graph of a Quadratic function is curve called a Parabola.
Exponential Function:
A function is said to be an exponential function if it is of the form
y = pq^x ,
where p is the initial value and q is the constant ratio.
Graph of Exponential function is steeper as the polynomial increases.
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How do you find the degree of a polynomial in precalculus?
Answer:
add up the exponents of each term and select the highest sum.
Pls help answer fast rapidly is of khan academy:
Answer:
expanded: 7+0.08
standard: 7.08
Step-by-step explanation:
The hundredths place is the second digit after the decimal, so 8 hundredths is 0.08.
Determine whether the relation is a function
Explain why or why not.
1. (9, -1) (4,2) (5,3) (8, -1) (3, 0)
The relation:
(9, -1) (4,2) (5,3) (8, -1) (3, 0)
Is a function, because each element of the domain appears only once.
Is the relation a function?A relation maps elements from a set, called the domain, into elements from another set, called the range.
Such that the element x being mapped into the element y is written as:
(x, y).
A relation is a function only if each element in the domain is mapped into only one element of the range.
Here we have the relation:
{ (9, -1) (4,2) (5,3) (8, -1) (3, 0)}
We can see that no element of the domain appears twice, so yes, this is a function.
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What is the radius of the sphere given by x2 y2 z2 − 6y 8z 0?
The sphere's radius is 5, and its center is at (0, 3, -4).
What is a sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions.
In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.
The radius of the sphere is denoted by the letter r, and the given point is its center.
List a few typical sphere examples from everyday life.
In everyday objects, sphere shapes can be found in the form of marbles, balls, oranges, yarn, and bubbles.
So, the center and radius of the sphere will be:
We have the sphere's equation, which is given by and has a radius of r.
(x - h)² + (y - k)² + (z - l)² = r² ...(1)
We must convert the following equation in order to determine the center and radius of the provided sphere.
x² + y² + z² - 6y + 8z = 0
By combining the x, y, and z terms and filling in the square, we obtain
x² + (y² - 6y + 9) +(z² + 8z + 16) = 9 + 16
(x - 0)² + (y - 3)² + (z + 4)² = 52
So, the sphere's center is at (0, 3, -4) and its radius is 5.
Therefore, the sphere's radius is 5, and its center is at (0, 3, -4).
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Complete question:
Find the center and radius of the sphere x2 + y2 + z2 - 6y + 8z = 0.
Write this ratio as a fraction in simplest form without any units.
Answer:
change 5 weeks to days(5*7)-35days
then convert the days to seconds
35*86400/10*86400
answer 7/2
Does an isosceles triangle have 3 acute angles?
Answer:
some do but not all
Step-by-step explanation:
some do but there is a right isosceles triangle where there is 45 45 and 90 degrees
hopes this helps please mark brainliest
Solve for x
2 1/2x - 3/4 ( 2x + 5 ) = 3/8
Please explain step by step on how I get this answer to solve x!
Answer:
4 [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
12. A factory needs to package 2,835 cartons
of orange juice in boxes. How many
more small boxes than large boxes are
needed to package the cartons of orange
juice?
Box Size
Small 15 number of cartons
Large. 35 number of cartons
The total number of cartons needed more to pack small 15 cartons than 35 large cartons is108 cartons.
What is the number of cartons needed?Division is defined as one of the four basic operations of arithmetic in mathematics.
The parameters for this question are:
Total number of cartons =2835
Number of small cartons needed = 15 cartons
Number of large cartons needed = 35 cartons
To package the orange juice in large cartons we need [tex]\frac{2835}{35} =81 cartons[/tex]
Also, to package 15 small cartons we need [tex]\frac{2835}{15} =189 cartons[/tex]
Number of more small cartons than large cartons is
Small cartons -large cartons
=189-81=108 more cartons.
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Explain how you can use compatible numbers to estimate the quotient of
925÷29.
HELPP PLEASEE ITS 50 POINTS TYY
Answer:
We can be able to use compatible numbers to estimate the quotient of 925/29 if the whole number that is part of the decimal is less than the divisor, we need to be able to rename the decimal.
Step-by-step explanation:
Evaluate the expression for j = –5, k = 2, and m = 3.
jk2 − m = ?
Answer: -23
Step-by-step explanation:
[tex]jk^2 -m=(-5)(2^2)-3=-5(4)-3=-20-3=-23[/tex]
Mark needs to cut a board to use for a project. The board is 12 feet long. He first has to cut off 24 feet from one end of the board. He
then cuts the remaining section of board into 4 equal pieces.
Which equation can be used to determine the the length of each equal piece?
04r-2-12
02-4-12
O2+4=12
O 4x+2¹-12
Next
The equation that best defines the length of the equal piece is 4x+2¹-12
How to determine an equation?We should know that an equation is a mathematical model that shows the equality of two sides of an expression
Based on the given condition 12-24=4*x
Applying multiplicative distribution -12=4x
Rearrange the equation 4x=-12
Calculate the product of the quotient x=-3
Now 24feet divided by -3 =-4
Since it deals with length =4
In conclusion the equation that determines the length of each equal piece is 4x+2¹-12
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david performed the following mathematical operation
1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].
We are given that polynomial [tex]$3 x^2+x-4$[/tex] is being divided by factor [tex]$(\mathrm{x}-1)$[/tex]
It is also said that when David perform the mathematical operation it gives remainder 0 .
Remainder 0 represents that divisor [tex]$(\mathrm{x}-1)$[/tex] is a factor polynomial [tex]$3 x^2+x-4$[/tex].
As x-1 is a factor of the given ploynomial, we can get one of the root of by setting it equal to 0 and solve for x.
Therefore,
x-1=0
Adding 1 on both sides, we get
[tex]$$\begin{aligned}& x-1+1=0+1 \\& x=1 .\end{aligned}$$[/tex]
Therefore, 1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].
Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.
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←
Diana has available 280 yards of fencing and wishes to enclose a rectangular area.
(a) Express the area A of the rectangle as a function of the width W of the rectangle.
(b) For what value of W is the area largest?
(c) What is the maximum area?
Answer:
(a) A = W(140 -W)
(b) W = 70
(c) 4900 square yards
Step-by-step explanation:
You want an expression for the rectangular area that can be enclosed by 280 yards of fence, if that area has width W. Further, you want the value of W that maximizes the area, and the size of that maximum area.
Perimeter expressionThe perimeter of the rectangle with length L and width W is ...
P = 2(L +W)
Then the length can be found from the width as ...
L = P/2 -W
For P=280, this is ...
L = 140 -W
(a) Area expressionThe area is the product of length and width:
A = LW
A = (140 -W)(W)
(b) Maximum areaThe area expression describes a downward-opening parabola with zeros at W=0 and W=140. The vertex (maximum) of the parabola is on the line of symmetry, halfway between these zeros. The value of W there is ...
W = (0 +140)/2 = 70
The area is largest for W = 70.
(c) AreaFor that value of W, the area is ...
A = (140 -70)(70) = 70² = 4900 . . . . . square yards
__
Additional comment
The generic solution to the area problem when fence is on all sides is that the shape is a square.
If the cost of fence is different for the different sides, the total cost in the east-west direction is equal to the total cost in the north-south direction when cost is minimized.
tic is an isosceles triangle with a vertex angle i if the measure of i90
Applying the definition of an Isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
In geometry, an isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.
An Isosceles triangle has a vertex angle and two equal base angles.
Given that triangle TIC is an isosceles triangle:
angle I is the vertex angle = 90 degrees
angle T is a base angle
angle C is also a base angle
Thus:
angle C and angle T are congruent or equal to each other.
Therefore,
Angle T = (180 - 90)/2
⇒ Angle T = 90/2
⇒ Angle T = 45 degrees.
applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
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Is a cubic graph exponential?
Yes, a cubic graph is an exponential.
What is Cubic Graph?
A cubic graph in the study of graph theory is a graph with all of its vertices having degree three. A cubic graph is a 3-regular graph, to put it another way. Trivalent graphs are another name for cubic graphs. A cubic bipartite graph is known as a bicubic graph.
What is Exponential?
The mathematical expression f(x)=exp or ex denotes the exponential function. Unless otherwise stated, the phrase usually refers to the positive-valued function of a real variable, though it can also be applied to complex numbers or extrapolated to other mathematical objects like matrices or Lie algebras.
Graphs of Exponential Functions if;
When the base is greater than 1, the exponential function has the following characteristics and you can easly understand from this :
The point is traversed by the graph (0,1)The domain only uses actual integers.It is between y>0.The graph is going up.The graph approaches negative infinity and becomes asymptotic to the x-axis.As x gets closer to positive infinity, the graph grows without bound.The chart is non-stop.The graph is rounded.Learn more about cubic graph exponential click here:
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A college student has budgeted $25 a month for phone services. If the telephone
company charges $17 a month for basic service and $0.05 a minute for each long
distance call, how many minutes can be spent on long distance calls each month?
(Define a variable, create an equation, solve using algebra, and answer in a sentence.)
Answer:
160 minutes can be spent on long distance calls each month.
Step-by-step explanation:
first we know that there is standard charge of $17 for basic service, $0.05 cost per minute with a budget of $25.
let's write that into an equation to solve for (a) which will be number of minutes.
17 + a(0.05) = 25
solving:
17 + a(0.05) = 25
carry across the 17 whilst changing the sign, or some people is also thought to minus on both sides to get rid of a certain variable.
a(0.05) = 25 - 17
a(0.05) = 8
carry across the multiplication of 0.05 which will then turn into division, or divide by 0.05 on both sides to remove it.
[tex]a = \frac{8}{0.05} [/tex]
a = 160
therefore 160 minutes can be spent on long distance calls each month.
You can redefine your answer more simply to hours by dividing by 60, which gives 2 hours and 40 minutes
An airplane is flying 700 feet above ground. From the plane to the base of the control tower, the angle of depression is 47◦ . How far away is ground directly underneath the plane to the control tower? Round your answer to the nearest tenth.
Using trigonometric ratio the distance to the control tower is 750.7ft
Trigonometric RatioIn trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.
The values of these trigonometric ratios can be calculated using the measure of an acute angle, θ in the right-angled triangle given below. This implies that the value of the ratio of any two sides of the triangle here depends on angle C.
Using trigonometric ratio, the distance is
tan θ = opposite / adjacent
tan 47 = x / 700
x = 700 tan 47
x = 750.7 ft
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Find the value of x. Then find the measure of each angle and write the answers in ascending order.
The value of x and the unknown angles of the triangle are as follows;
x = 1180 degrees117 degreesHow to find angles in a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Therefore, let's find the value of x using the exterior angle theorem.
Hence,
37 + 3x + 47 = 5x + 62
3x - 5x + 37 + 47 = 62
-2x = 62 - 37 - 47
-2x = -22
x = -22 / -2
x = 11
Therefore, the angles are as follows:
3x + 47 = 3(11) + 47 = 33 + 47 = 80 degrees
5x + 62 = 5(11) + 62 = 55 + 62 = 117 degrees
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The equation that models the function is P(t) = 20400(1,09)⁺ and the fox population in 2008 is 40648
The equation of the functionFrom the question, we have the following parameters that can be used in our computation:
Initial population of fox = 20400
Rate of growth = 9 percent per year
These parameters can be presented as
Initial population of fox, a = 20400
Rate of growth, r = 9%
An exponential function is represented as
P(t) = a(1 + r)⁺
So, we have:
P(t) = 20400(1 + 9%)⁺
Evaluate
P(t) = 20400(1,09)⁺
The population in 2008Recall that
t = 0 in 2000
So, the value of t in 2008 is
t = 2008 - 2000
t = 8
Substitute t = 8 in P(t) = 20400(1,09)⁺
So, we have
P(8) = 20400(1.09)⁸
Evaluate
P(8) = 40648
So, the population is 40648
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Nathan is building a toolshed with a rectangular floor. The area of a rectangle is given by the formula 1 w, where I represents
the length, and w represents the width. The floor of the shed will have measurements of either / = 9 and w =
= 7 or/= 8 and
w = 8. What is the area of the larger floor?
O63
O 64
O 56
O 72
The area of the larger floor is 64 square units when w = 8 and l = 8. which is the correct answer would be an option (B).
To compare the values, we must first calculate each given situation. The area of any given rectangle is length times width.
If w = 7 and l = 9
A = l × w = 8 × 6 = 48
If w = 8 and l = 8
A = l × w = 8 × 8 = 64
So, the second case would obtain a larger area.
Therefore, the area of the larger floor is 64 square units when w = 8 and l = 8.
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What are the 4 types of properties?
There are four basic properties of numbers: commutative, associative, distributive, and identity.
1.Commutative Property
a. Addition
. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.
3 + 5 = 8 or 5 + 3 = 8
b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.
3 x 5 = 15 or 5 x 3 = 15
2.Associative Property
a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.
6 + (4 + 3) = 13 or (6 + 4) + 3 = 13
b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.
6 x (4 x 3) = 72 or (6 x 4) x 3 = 72
3.Distributive Property
The sum of two numbers times a third number is equal to the sum of each addend times the third number.
5 x (7 + 2) = 45 or 5 x 7 + 5 x 2 = 45
4.Identity Property
a. Addition. The sum of any number and zero is that number.
12 + 0 = 12
b. Multiplication, The product of any number and one is that number.
18 x 1 = 18
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One integer is 2 times another. If the product of the two integers is 32, then find the integers
Answer:
The integers could be 8 and 4, just checked with a calculator
Joseph has $1.45 worth of nickels and dimes. He has a total of 17 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Joseph has.
The number of nickels and the number of dimes that Joseph has are 12 and 5 respectively.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
Let the no. of nickels be N and no. of dimes be D.
∴ N + D = 17...(i) and 0.05N + 0.1D = 1.45...(ii)
Multiplying (ii) by 100 we get 5N + 10D = 145...(iii)
Now multiply (i) by 5 we get 5N + 5D = 85...(iv)
Now subtracting (iv) from (iii) we get,
5D = 60.
D = 12 hence N = 5.
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A line with a slope of 1 passes through the point (5, 3). What is its equation in slope "-intercept" form?
Answer: y=x−2 y = x − 2
Step-by-step explanation:
Coordinate Plane
help asappp tyyy
Using cartesian coordinate system, the points are plotted on the graph below which shows A in the fourth quadrant, B in the third quadrant, C in the first quadrant, D and E in the second quadrant and F on the first quadrant.
Graph on a coordinate planeA coordinate graph is a graph with two axes which are placed perpendicular to each other. These two axes are called x-axis and y-axis. The vertical line is the y-axis and the horizontal line is the x-axis. It is also called a coordinate plane, a Cartesian plane, and a Cartesian coordinate system.
Kindly check the attached graph below
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Answer: plot point
Step-by-step explanation: plot point, quadrant or axis be smart and learn nivia.
is x^2+x+1=0 linear?
Answer:
No.
Step-by-step explanation:
Because the equation has an exponent, it is quadratic, and not linear.
Answer:1
Step-by-step explanation:
A ball is dropped from a height of 20 feet. Each time the ball bounces it returns to 7/9 of the height it fell from. Let an represent the maximum height of the ball on the nth bounce.
A) Find a formula that describes an. Express the common ratio as a fraction. Hint: Use an = a1r^n-1 and place r in parentheses!
an = _____________
B) What is the maximum height of the ball on the 6th bounce? Round your answer to three decimal places.
_______________ feet
(A) The formula for nth bounce is [tex]a_n = 20 (7/9)^{n}[/tex].
(B) 4.43 feet is the maximum height of the ball on the 6th bounce.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
Given that,
The height from where the ball is dropped = 20 feet.
Also, the ball bounces and returns to 7/9 to its original height.
(A)
The representation of the maximum height of the ball on the nth bounce can be given as
[tex]a_n = 20 (7/9)^{n}[/tex]
(B)
The maximum height of the ball on the 6th bounce = 20 (7/9)⁶ = 4.43 feet
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How do you prove a trapezoid is isosceles?
Answer:
A trapezoid is isosceles if and only if its diagonals are congruent. So if we can prove that the bases are parallel and the diagonals are congruent, then we know the quadrilateral is an isosceles trapezoid, as Cool Math accurately states.
Step-by-step explanation:
What are the types of inverse?
The various types of inverse function are the inverse of trigonometric functions, rational functions, hyperbolic functions and log functions
If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f⁻¹or F⁻¹.
A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.
The various types of inverse function are:
Inverse Trigonometric Functions : The inverse trigonometric functions are also known as arc function as they produce the length of the arc.Inverse Hyperbolic Function : Just like inverse trigonometric functions, the inverse hyperbolic functions are the inverses of the hyperbolic functions. There are mainly 6 inverse hyperbolic functions exist which include sinh⁻¹ , cosh⁻¹, tanh⁻¹, csch⁻¹, coth⁻¹, and sech⁻¹Inverse Logarithmic Functions and Inverse Exponential Function : The natural log functions are inverse of the exponential functions.To know more about The inverse of function here
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A ball is dropped from a height of 10 ft and bounces 83% of its previous height on each bounce. How high off the ground is the ball at the top of the 4th bounce?
Answer:
The height of the 4th bounce would be 4.7458321; rounded would be 4.8.
Step-by-step explanation:
We can figure this question out by first converting the 83% into a decimal, by bringing back 2 decimal places:
0.83.
And then setting up this equation:
0.83 x 10 = 8.3
Now, this is for 1 bounce. We have to do this 4 more times:
0.83 x 8.3 = 6.889
3rd time:
0.83 x 6.889 = 5.71787
4th time:
0.83 x 5.71787 = 4.7458321.
Now, we can round this answer to:
4.8
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