The linear equation f(x) is 4x - 10 and the quadratic equation f(k) is -5/2k^2 + 4k - 1 for the two given points.
The linear equation can be found using the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept. To find the slope (m) we can use the two points given:
m = (y2 - y1) / (x2 - x1) = (18 - 2) / (7 - 3) = 16/4 = 4
The y-intercept (b) can be found using one of the points and the slope:
b = y - mx = 2 - 4(3) = -10
So the linear equation in standard form is:
f(x) = 4x - 10
For the quadratic equation, we know that it's in the form of y = ax^2 + bx + c. We have 2 points, so we have 2 equations with 2 unknowns. We can use this information to solve for a, b and c.
Let's (3,2) point 1 and (7,18) point 2.
f(k) = ak^2 + bk + c....(1)
point 1: f(3) = 2 = 9a + 3b + c...(2)
point 2: f(7) = 18 = 49a + 7b + c...(3)
Now we have 2 equations and 3 unknowns.
using theirs first equation and substitute it in the second and third equation
18 = 49a + 7b + c
2 = 9a + 3b + c
c = 2 - 9a - 3b
18 = 49a + 7b + (2 - 9a - 3b)
18 = 49a + 7b + 2 - 9a - 3b
18 = 40a + 4b + 2
16 = 40a + 4b
now this equation is used to solve for a and b
b = (16 - 40a) / 4
so a,b and c are
a = -5/2
b = 4
c = -1
so the quadratic equation in standard form is:
f(k) = -5/2k^2 + 4k - 1
4x - 10 is the linear equation f(x) and -5/2k^2 + 4k - 1 is the quadratic equation f(k) for the two given points.
To know more about quadratic equation :
https://brainly.com/question/28038123
#SPJ4
help help help help plsss i need this now i don't have time
For this we can use an equation of y=mx+b, b will equal what she started with, and m will be how much she saves each week
Using this, we now can use the equation Y=15x+30, y equals the total she has saved, and x equals the weeks.
You should be able to use this equation to solve the rest now!
a circular pool has a radius of 7.5 ft the calculate the length of the trim needed to go around the entire edge of the pool
Answer:
pretty sure it would be 30 ft.
Step-by-step explanation:
What are the 3 different polynomial equation?
The 3 different polynomial equations are linear polynomial equations, quadratic polynomial equations, and cubic polynomial equations.
A polynomial equation is one where a polynomial is set equal to zero. i.e., it is an equation created with variables, non-negative integer exponents, and coefficients together with operations and an equal sign.
A polynomial equation is always like "polynomial = 0". Algebraically, it is of the form p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₁ x¹ + a₀x⁰ = 0, where
aₙ, aₙ₋₁, ...., a₁, a₀ are coefficients and all these numbers are real numbers.
'x' is the variable.
p(x) means "polynomial in terms of variable x"
'n' is a non-negative integer, it is the degree of p(x).
To know more about polynomial, here
https://brainly.com/question/11536910
#SPJ4
Select the correct answer.A wooden board that is 108 inches long is cut into two equal parts. What is the length of each part in feet
4.5 is the length of each part in feet. This can be solved by using the concept of feet.
What is feet?foot, plural feet, any of a wide range of ancient, medieval, and modern linear measurements (often 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.
The foot measured [tex]11^{\frac{1}{42}[/tex] inches in antiquity. The typical man's foot measures 12 inches in length nowadays.
Given that:
The length of the wooden board is given as = 108 inches.
As it is cut in 2 equal parts, it becomes: 108/2 = 54 inches in each
We have to calculate the length of each part in feet, so divide 54 by 12.
As we know,
12 inches = 1 feet
Thus, 54 inches = 54/12 feet = 4.5 feet
So, the length of each part is 4.5 feet.
To know more about feet refer to:
https://brainly.com/question/876758
#SPJ4
If 7 pounds of candy cost $16.17. How much does 1 pound of candy cost?
Answer:
$2.31
Step-by-step explanation :
$16.17 divided by 7
How would I find the range btw im only allowed a Ti-84 calculator So pls tell me how to solve this without using any stepbystep caulculators or desmos
Is the answer ASA?
Please explain!
Answer:
No, it is AAS.
Step-by-step explanation:
By vertical angle theorem ∠KLJ≅∠MLN.
And the given congruent sides are not between the two congruent angles, therefore it cannot be ASA.
Triangle KLJ ≅ Triangle MLN
Which polynomial is prime?
O x3 + 3x2 - 2x - 6
O x° - 2x- + 3x - 6
O 4x4 + 4x3 - 2x - 2
O 2x + x3-x+2
Morgan bought 95 roses from the florist for her wedding. The roses cost $1.75 each, including sales tax. If Morgan gives the florist $200, how much change should she get back?
Answer:
33.75
Step-by-step explanation:
1.75*95 = 16 6.25
200 - 166.25 = 33.75
Exercise: Use the method of mathematical induction to prove that if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1)
if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1) IS 1
What is meant by integer?An integer, which is pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Examples of integers include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are examples. The set of whole numbers and their antipodes is known as the integers. The set of integers excludes fractions and decimals. For instance, 2,5,0,12,244,15, and 8 are all numbers. Any positive or negative number that does not contain fractions or decimal places is known as an integer, often known as a "round number" or "whole number." For instance, the numbers 3, -10, and 1,025 are all integers, whereas the numbers 2.76 (decimal), 1.5 (decimal), and 3 12 (fraction) are not.P(n) :
1²+ 2² + 3² + … +n² = 1/6n(n+1)(2n+1)
P(1) :
[tex]1^2=\frac{1(1+1)(2(1)+1)}{6}[/tex]
[tex]1=\frac{6}{6}=1[/tex]
∴ LHS = RHS
Assume P(k) is true
P(k):
To learn more about integer, refer to:
https://brainly.com/question/929808
#SPJ1
4x=3x+5 need help with this problem!
Answer:
its isssssssss x=5
Step-by-step explanation:
.......
Answer:
it's 5
Subtract
3
3x
3x
from both sides of the equation
4
=
3
+
5
4x=3x+5
4x=3x+5
4
−
3
=
3
combine the like terms 4
−
3
=
3
+
5
−
3
}{-3x}}=3x+5-3x
4x−3x=3x+5−3x
1
=
3
+
5
−
3
+
5
−
3
Why do we not feel Earth rotation and revolution?
Earth's rotation and revolution are both very slow motions, so slow that we don't feel them. The rate of Earth's rotation is about 1,000 miles per hour, and the speed of its revolution is about 67,000 miles per hour, but both of those speeds are so slow that we don't feel any movement or acceleration.
Earth's rotation and revolution are both very slow motions, so slow that we don't feel them. The rate of Earth's rotation is about 1,000 miles per hour and its revolution is about 67,000 miles per hour, but both of these speeds are too slow to be felt.Earth's rotation and revolution are both very slow motions, so slow that we don't feel them. The speed of Earth's rotation is about 1,000 miles per hour, and the speed of its revolution is about 67,000 miles per hour, but both of those speeds are so slow that we don't feel any movement or acceleration.
Learn more about rate here
https://brainly.com/question/13481529
#SPJ4
What is the slope of this line? (5 points)
Show all work.
Slope of the line AB is 7/6.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the given graph the coordinates of A are (4, 3) and B is (-2, -4)
Slope AB=-4-3/-2-4
=-7/-6
Slope=7/6
Hence, slope of the line AB is 7/6.
To learn more on slope of line click:
https://brainly.com/question/14511992
#SPJ1
Emily and four friends went out for pie and ice cream. The total cost of the ice cream was $5. If each person paid $8, what was the total cost of the pie?
Which of the following is a like radical to 3x5?
5y
3(5x)
y5
Answer:
y[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Like radicals are radicals that have the same radical (the number into the square root) and the same radicand (the number above the root)
Here, only the last expression [tex]\sqrt{5}[/tex] can be chosen.
what is the value of x?
Answer:
x = 20
Step-by-step explanation:
All sides are equal ( as shown by the markings )
An equilateral triangle's angles = 60
Ask self, what can I multiply by 3 to get 60?
Alice is playing a game in which she will roll 4 6-sided dice at the same time. She gets 5 points for each die that shows an even result. Let x represent the total number of points awarded on any given toss of the dice. What is the expected value of x? A. 1/2 B. 2 C. 10 D. 15 E. 20
The number of points is simply 5 times this random variable, and E(C*Y) = C*E(Y), where C is a constant and Y is a random variable, according to expected value principles. As a result, E(X) = 5*2 = 10.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
The number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).
The expected value of this random variable is n*p = 4*1/2 = 2.
The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable. Thus E(X) = 5*2 = 10.
To know more about probability,
https://brainly.com/question/30034780
#SPJ4
Emily invested $810 in an account paying an interest rate of 3 and 5/8% compounded monthly. Jûlian investéd $810 in an account paying an interest rate of 3 and 1/4% compòunded continuoûsly
Answer:
$1752Step-by-step explanation:
------------
Added below
Timmy is rolling a 6 sided die what is the sample space.
A.1,2,3
B.1,2,3,4,5,6
C.1,2,3,4,5,6,7
D.1,2,3,4,5,5,6
Answer:
b. 1,2,3,4,5,6
bc a dice has 6 sides
I HAVE A F PLEASE HELP ASAP 100 POINTS
construct a line that goes through points
and . Label the line g.
Trejo says that if you know the x-intercepts,
y-intercepts, domain, and range of a
function then you automatically know the x-
intercepts, y-intercepts, domain, and range
of its inverse. Hilary disagrees. She says you
know the intercepts but that is all you know
for sure. Who is correct? Justify your
answer.
Trejo is correct, because if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
Trejo says that if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.
But, Hilary disagrees, She says you know the intercepts but that is all you know for sure.
Now,
We know that;
In a function, If if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.
Thus, The Trejo is correct.
Learn more about the function visit|:
https://brainly.com/question/11624077
#SPJ1
NP, PM, and MN are all midsegments and bisect each side.
NP = 12
MP=2x
RQ = 5x-1
SQ=6x
Solve for x.
Label each midsegment with its correct measure:
NP, PM, and MN are all midsegments and bisect each side.
value of x = 5 unit
NP = 12
MP=2x
RQ = 5x-1
SQ=6x
Using Midsegments of a Triangle
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle
Triangle Midsegment Theorem
Using Midsegments of a Triangle
Theorem 5-1 Triangle Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side and is half as long.
Triangle Midsegment Theorem A segment whose endpoints are the
midpoints of two sides of the triangle
Midsegment
Base
Midsegment = ½ of Base
M = ½ b
NP =1/2(RQ)
12 =1/2(5x-1)
12* 2 = 5x-1
24 =5x-1
24+1 =5x
25 =5x
x=25/5
x = 5 unit
NP, PM, and MN are all midsegments and bisect each side.
value of x = 5 unit
To know more about midsegments visit brainly.com/question/2273557
#SPJ4
Which expression is equivalent to y4 – 100?
Answer:
4y-100
2(2y-50)
hope this helps
have a good day :)
Step-by-step explanation:
Solve the system of equations by the addition method.
4x-5y=22
3x +2y = - 18
Using the provided equations, Applying the addition method in the system of equations, The answer is x=-2 and y =-6.
What do you mean by equation?An equation is a statement of equality between two expressions, usually containing one or more variables. Equations can be used to express mathematical relationships and can be solved to find the value of the variables. Equations can take many forms, such as linear equations, quadratic equations, and differential equations. They can also be represented graphically.
What is the addition method to solve system of equations?The addition method to solve a system of equations is a way to solve a system of two linear equations by adding them together. The goal is to eliminate one variable by adding or subtracting the equations. We can eliminate one variable by adding the equations together. To do this, we'll add the left-hand side of the first equation to the left-hand side of the second equation and add the right-hand side of the first equation to the right-hand side of the second equation. It is important to note that the addition method works only when the coefficients of the variable you want to eliminate are opposite in sign.
4x-5y=22
3x+2y=-18
multiplying first equation with 3 and second equation with 4 and subtracting them , we eliminate x and solve for y,
y=-6
put y=-6 in first equation , we get x,
x=-2
To learn more about equations visit:
https://brainly.com/question/29657983
#SPJ1
y=x^2+3x+4 function, what is the equation of point x=1
А. 5х + 3
В. 5х + 1
с. 5 — 1
D. 5х + 2
E. 5 – 7
Carlos had $20 before he bought 4 bottles of water. The bottles of water cost d dollars
each. Which expression represents how much money Carlos has after buying the
bottles of water?
Answer:
4d-20
hope this helps
Step-by-step explanation:
State the Domain & the Range.
g(x) = |x – 1| + 2
Domain:
Range:
Answer:
domain: (-oo,oo)
range:[2,oo)
Please help! WILL GIVE BRAINLIEST
Answer:
71
Step-by-step explanation:
I found the area by spliting the figure into the triangle, square, and rectangle
triangle = .5(14*5)=35
square = 2*2=4
rectangle = 8*4=32
35+4+32=71
hope this is right:)
A chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form \frac{a\pi+b\sqrt{c}}{d\pi-e\sqrt{f}}, where a, b, c, d, e, and f are positive integers, a and e are relatively prime, and neither c nor f is divisible by the square of any prime. Find the remainder when the product abcdef is divided by 1000.
The remainder when 2 is divided by 1000 is 2
Let O be the center of the circle, R be the length of the radius, and let the chord be AB with midpoint M. Let x be the distance from O to M, then the length of the radius OM is R/2 and the length of the chord AB is 2x.
Since the chord is perpendicular to the radius at the midpoint, we know that the radius bisects the chord. Therefore, the two segments MO and MB are congruent and have length x.
The area of the larger region is the area of the sector OMB, which is (1/4) of the area of the circle. The area of the smaller region is the area of the triangle OMA, which is (1/2) of the area of the sector OMA.
The ratio of the larger region to the smaller region is (1/4) : (1/2) = 2 : 1.
So, the area of the larger region is twice the area of the smaller region.
We can see that abcdef = 21111*1 = 2, the remainder when 2 is divided by 1000 is 2. Thus, the answer is \boxed{002}.
To know more about Circle Cord Ratio visit :
https://brainly.com/question/11013575?referrer=searchResults
#SPJ4