The linear function with values of f(-1)=8 and f(5)=6 is f(x) = [tex]\frac{-x+23}{3}[/tex].
What is linear function?
A straight line on the graph has the equation or formula y = f(x) = px + q is linear function .One independent and one dependent variables are present. X and Y are the independent and dependent variables, respectively. P is the y-intercept or constant term, and it also represents the value of the dependent variable. A straight line on the coordinate plane is represented by a linear function.
Here the given values are f(-1)=8 and f(5)=6.
We know that f(x)=y , Then the points are (-1,8) and (5,6).
Using slope formula ,
=> slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = -2/6=-1/3
Now using slope formula,
=> [tex]y-y_1=m(x-x_1)[/tex]
=>y-8=-1/3(x+1)
=>3y-24=-x-1
=> 3y=-x+23
=> y = [tex]\frac{-x+23}{3}[/tex]
Hence the linear function is f(x) = [tex]\frac{-x+23}{3}[/tex].
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not really sure what to do here??
Answer:
[tex]d=-6[/tex]
[tex]a_9=-49[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]-1[/tex] and the second term is [tex]-7[/tex], then each successive term in the sequence is [tex]6[/tex] less than the previous term. The common difference is [tex]-6[/tex] ( [tex]d=-6[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=-6n+5[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=-6(9)+5[/tex]
[tex]a_9=-54+5[/tex]
[tex]a_9=-49[/tex]
The regression equation for 2 variables is y = -2.6 x + 10 If the value of R2 is 0.810, what is the value of R?
If the value of R² in the regression equation is 0.810, the value of R is 0.9
How to determine the value of r?From the question, we have the following parameters that can be used in our computation:
Regression equation: y = -2.6x + 10
Value of R2 = 0.810
Rewrite the above parameters properly
So, we have the following representation
y = -2.6x + 10
R² = 0.810
The variable r² represents the coefficient of determination
Recall that
R² = 0.810
This gives
r² = 0.810
Take the square roots of both sides
r = 0.9
Hence, the value of r is 0.9
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92≤x≤9? I need help with this fast thankyou
Answer:
yes
Step-by-step explanation:
because 4
Answer:
Step-by-step explanation:
average rate of change
[tex]=\frac{25-(-10)}{9-2} \\=\frac{35}{7}\\=5[/tex]
Which inequality is represented by the graph?
5 - 3 -2 -1 0 1 2 3
-3
(1) x>-1
(3) *<-1
(2) x≤-1
D
(4) x ≥-1
4
gering
5
Answer:
answer,(2)x≥-1
Step-by-step explanation:
it was right
5x10^-10/3x10^-9
1x10^-9/3.5x10^-9
Answer:
1.667×10^-12.857×10^-1Step-by-step explanation:
You want the result of a division operation performed on numbers written in scientific notation.
In each case, the result number will have a repeating decimal fraction. We show 4 significant figures in the answer. The number of significant figures you need to use will depend on what you're using the answer for. If you are required to match the precision of the numbers here, you will want to use 1 significant figure.
The rules of exponents apply, so the exponent of the result will be the difference of the exponents of numerator and denominator. As always, if the numerator mantissa is smaller than the denominator mantissa, the result will be a fraction, so adjustment of the exponent will be necessary.
5×10^-10/(3×10^-9)= (5/3)×10^(-10-(-9)) = 1.667×10^-1
1×10^-9/3.5×10^-9= (1/3.5)×10^(-9-(-9)) = 0.2857×10^0 = 2.857×10^-1
__
Additional comment
Any scientific or graphing calculator and any spreadsheet can accept input in scientific notation and format the output in the same way.
You need to be careful with the way you enter the multiplier. Most calculating platforms accept the E notation shown in the attachment. If you use multiplication (×10^-9, for example), then the denominator number will need to be enclosed in parentheses. The third line of the second attachment shows the result of not using parentheses: the multiplier intended for the denominator instead multiplies the result of the division. (This behavior is required by the Order of Operations.)
Rewrite as equivalent rational expressions with denominator (5c+9)(c−3)(c−8): 8/5c^2-6c-27, 2c/5c^2-31c-72
The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)].
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given expression,
8/(5c² - 6c - 27) , 2c/(5c² - 31c - 72)
Now, take the first denominator,
5c² - 6c - 27 = 5c² - 15c + 9c - 27
⇒ 5c(c - 3) - 9(c - 3)
⇒ (c - 3)(5c - 9)
Take the second denominator
5c² - 31c - 72 = 5c² - 40c + 9c - 72
⇒ 5c(c - 8) + 9(c - 8)
⇒ (c - 8)(5c + 9)
Therefore, the expression converts as,
8/[(c - 3)(5c - 9)] , 2c/[(c - 8)(5c + 9)]
8/[(c - 3)(5c - 9)] = 8(c - 8)/[(c - 3)(5c - 9)(c - 8)]
2c/[(c - 8)(5c + 9)] = 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]
The denomiantor of both expression are same.
Hence "The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]".
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The structured question below,
Solve for x.
Please !!!
Step-by-step explanation:
6x-4+60=14x-8
6x+56=14x-8
8x=64
x=8
On what intervals is the function increasing?
Indicate intervals on the x-axis using the Ray tool for intervals that extend to infinity and the Segment tool for bounded intervals.
Graph a ray by selecting the endpoint followed by a point on the ray. Graph a segment by selecting an endpoint followed by the other endpoint.
Answer:
[-7, - 2] and [3, 7]--------------------------------------
The graph has two local maximums and two local minimums.
The intervals between those points are the increasing intervals.
Refer to the attached, where the intervals are marked.
The intervals are
x = [-7, - 2] and [3, 7]p=(-3,7); m=-1 graph line containing the point p and having slope m.
The equation of the line is x+y-4=0.
What is an equation?
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Main Body:
we know that one point form of a line is
y-y₁= m(x-x₁) , where m= slope
now given is a point (-3,7) and m=-1
y-7 =(-1)(x+3)
x+y-4=0
Hence the answer is x+y-4 =0
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What are the coordinates of the point that is one half the distance between A(-1, -2) and B(6, 12)?
Enter your answer by filling in the boxes.
The coordinates of the point that is one half the distance between A and B is (5/2, 11/2)
How to determine the coordinates of the point that is one half the distance between A and B?
The point with the distance that is one half the distance between A and B is the midpoint of A and B.
The coordinate of the midpoint of a line is the half x values and y values. Thus: Xm = (X1 + X2)/2 and Ym = (Y1 + Y2)/2
where m is the midpoint
Given: A(-1, -2) and B(6, 12)
X1 = -1, Y1 = -2 and X2 = 6, Y2 = 12
Xm = -1+6 /2 = 5/2
Ym = -2+12 = 11/2
Therefore, the coordinates of the point that is one half the distance between A(-1, -2) and B(6, 12) is (5/2, 11/2)
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In Exercises 27-30, give the measure of the angle in radians and
degrees. Give exact answers whenever possible.
sin¹ (0.5)
The measure of the angle for the given trigonometric function is 30°.
Given that, [tex]sin^{-1}(0.5)[/tex].
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.
Trigonometry angle can be expressed in terms of trigonometric ratios as,
θ = [tex]sin^{-1[/tex] (Perpendicular/Hypotenuse)
θ =[tex]sin^{-1[/tex] (0.5)
= [tex]sin^{-1[/tex] (1/2)
= 30°
Therefore, the measure of the angle for the given trigonometric function is 30°.
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The sum of a number and 4 times the number
Write two equivalent expressions for each statement.
Let the number be n.
Then the expression is:
The sum of a number and 4 times the numbersum = n + 4nsum = 5nAnswer:
4x + x5xStep-by-step explanation:
Forming the expression,
→ 4x + x
Let's solve the expression,
→ 4x + x
→ 5x
Hence, the answer is 5x.
An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+32t+20, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Using differentiation, 36 feet is the maximum height, in feet, that the object will reach.
In the given question,
An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground.
The position of the object can be modeled using the function [tex]f(t)=-16t^2+32t+20[/tex], where t is the time in seconds and f(t) is the height, in feet, of the object.
We have to find the maximum height, in feet, that the object will reach.
The given function is [tex]f(t)=-16t^2+32t+20[/tex].
To find the maximum height we differentiate the function with respect to t
[tex]\frac{df}{dt}=-32t+32[/tex]
As we know that at the maximum point the slope of the tangent is zero.
So df/dt = 0
So -32t+32=0
Subtract 32 on both side
-32t+32-32=0-32
-32t=-32
Divide by -32 on both side
-32/-32 t = -32/-32
t=1
Therefore at t=1 the function have maximum value. So we put t=1 in the given equation.
[tex]f(1)=-16(1)^2+32\times1+20[/tex]
f(1)=(-16)×1+32×1+20
Simplifying
f(1)=-16+32+20
f(1)=36 feet.
Hence, 36 feet is the maximum height, in feet, that the object will reach.
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Use a table of areas to obtain the shaded area under the standard normal curve.
The shaded area under the standard normal curve is 2.58%.
According to z-score table,
Area for < 2.23 = 0.9871
Area for >2.23 = 1 - 0.9871
= 0.0129
Area for < 2.23 = 0.0129
Total area = 0.0129 + 0.0129
= 0.0258
Area percent = 0.0258*100
= 2.58%
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How many ways can the letters in the word CHEWY be arranged to form a five letter code
Answer:
60 ways;
GOOD LUCK!
Step-by-step explanation:
The word CHEWY has 5 letters, Therefore, it can be arranged in 5!/2! = 120/2 = 60 ways.
a piece of pipe is 40in. long. It is cut in to 3 pieces. the longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece. Find the lengths of all 3 pieces of pipe.
The length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.
According to the question,
We have the following information:
A piece of pipe is 40in. long. It is cut in to 3 pieces. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece.
Let's take the length of middle sized piece to be x inches.
Length of longest piece = 3x inches
Length of shortest piece = (3x-23) inches
Now, we have the following expression:
x+3x+3x-23 = 40
7x-23 = 40
Adding 23 on both the sides:
7x = 40+23
7x = 63
Dividing by 7 on both the sides:
x = 63/7
x = 9 inches
Length of longest piece = 3*9 inches
Length of longest piece = 27 inches
Length of shortest piece = (27-23) inches
Length of shortest piece = 4 inches
Hence, the length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.
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The population of city A is 24% less than the population of city B, so city A's population is _____% of city B's.
Answer:
76%
Step-by-step explanation:
100%-24%=76%
y varies inversely with the square x. If y =
-4 when x =
-2, find y when x= 7.
The value of y is - 0.326 when x = 7.
What are ratio and proportion?A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is typically expressed as x: y or x/y, although it may alternatively be read as x is to y.
Comparatively speaking, a proportional equation states that two ratios are comparable. A ratio is expressed as x: y: : z: w and is understood to mean that x is to y as z is to w. Here, w and y are not equal to 0, therefore x/y Equals z/w.
A connection between two quantities is said to be in inverse proportion if one quantity rises while the other falls, and vice versa. As a result, an inverse ratio is expressed as y ∝ 1/x.
The general equation of proportion is given by
y = k/x²
-4 = k/(-2)²
k = -4(4)=-16
y = -16/x²
When x=7, then
y= -16/49
y= - 0.326
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a packet of crisps weighs 32 grams to the nearest gram. a multipack of crisps contains 10 packets. work out the least and the greatest weights of the multipack. you can ignore the weight of the multipack wrapper
If a multipack of crisps contains 10 packets. the least and the greatest weights of the multipack is 315, 325.
How to determine the least and greatest weight?Range = 31.5≤ x < 32.5
Range = 31.5≤ 10 < 32.5
Hence,
Lowest and greatest possible for 32 grams
Lowest possible = 31.5 grams
Greatest possible =32.4 grams
Since multipack of crisps contain is 10 packets hence.
Least weight = 31.5 grams × 10
Least weight =315
Greatest weight = 32.5 grams × 10
Greatest weight = 325
Therefore 315 and 325 are the weight.
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A couple bought a rental house for $195,000 it’s assessed value was $180,000 if the tax rate is $1.50 per $100 of assessed value what is the monthly contribution the lender will require for taxes round to the nearest cent
Step-by-step explanation:
there is no interest and such involved. it is a straight forward calculation to allow the lender to accumulate enough funds (= the ESCROW account as part of the mortgage account structure) to be able to pay the taxes once a year on behalf of the owners.
so, the tax is $1.50 for every $100 of the assessed value of the house.
how many $100 units are in that value ?
180,000 / 100 = 1,800 units.
that means the tax for that house is
1800 × 1.5 = $2,700
in order for the lender to accumulate $2,700 in the ESCROW account in a year (= 12 months), the monthly contribution has to be
2700 / 12 = $225.00
What is the equation of this graphed line?
Answer:
y = 2x +2
Step-by-step explanation:
You want the equation of the line through points (-4, -6) and (2, 6).
SlopeThe slope of the line is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (6 -(-6))/(2 -(-4)) = 12/6 = 2
Point-slope equationThe point-slope equation of a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Using the point (2, 6) and the found value of slope, an equation for the line can be written:
y -6 = 2(x -2) . . . . point-slope equation for the line
Slope-intercept equationSolving this equation for y and simplifying, we get the slope-intercept equation of the line.
y = 2x -4 +6 . . . . . eliminate parentheses, add 6
y = 2x +2 . . . . . . . . simplify; slope-intercept equation
lee has seven 5-dollar bills and 6 quarters
in his pocket. How much money would he have
left in his pocket if he buys a leather jacket
worth $35.20.
Answer:
Lee would have $1.30 left.
Step-by-step explanation:
7 x 5 = $35
6 x .25 = $1.50
Altogether, Lee has $36.50 before buying the jacket
$36.50 - 35.20 = $1.30
Select the equation of the graph line above. (A) y = x + 5 (B) y = 3x + 5 (C) y = x - 5 (D) y = 3x - 5
Answer: (D) [tex]y=3x-5[/tex]
Step-by-step explanation:
Using the points (0, -5) and (2, 1), the slope of the line is [tex]\frac{-5-1}{0-2}=3[/tex].
Since the y-intercept is -5, the equation is [tex]y=3x-5[/tex].
Does the compound event consist of two mutually exclusive events?
Two dice are rolled. The sum of the dice is a 3 or a 9.
Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4
What is meant by probability?Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty.
A compound event is made up of two separate events.
Here is a table of probable sums of two die rolls. Die 1 and Die 2 values are listed along the side and top. The figures are roughly near the middle. The sum of Die 1 = 2 and Die 2 = 2 is 4, for example.
Die 2
Die1 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Rolling two dice yields 6 * 6 = 36 possible outcomes, or 36 possible sums. There are 36 occurrences in the sample space.
Looking at the table, a 3 or a 9 happens as the sum 9 times, resulting in 9 of the 36 potential occurrences having a sum of 3 or 9.
Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4
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At the beginning of a journey, the fuel tank of a car was 34 full. When the car reached its destination, it had consumed 60% of the gasoline in the tank. The full capacity of the fuel tank was w gallons.
a Enter an algebraic expression for the amount of gasoline left in the fuel tank.
gal
b If w = 15.5, how much gasoline was left in the tank at the end of the journey?
gal
a) An algebraic expression for the gasoline left in the fuel tank is L = 0.4w.
b) If w = 15.5, the amount of gasoline left in the tank at the end of the journey was 6.2 gallons.
What is an algebraic expression?An algebraic expression is a mathematical statement that combines constants and variables together with mathematical operands.
The mathematical operands include addition, subtraction, division, multiplication, etc.
Let L = the amount of gasoline left
Let the full capacity of the fuel tank = w gallons
Gasoline consumed on the journey = 60% = 0.6
Equation:L = w - 0.6w
L = 0.4w
Solution:If w = 15.5
L = 0.4(15.5)
= 6.2 gallons
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Use point-slope form to write the equation of a line that passes through the
point (14,-17) with slope -2.
Answer:
[tex]y+17=-2(x-14)[/tex]
Step-by-step explanation:
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].
A manufacturer of fax machines find that the cost (in dollars) generated by manufacturing x
units per week is given by the function C(x) = 0.15x²-39x+4500. How many units should
be manufactured to minimize the cost?
130 units should be manufactured to minimize the cost.
How to solve a quadratic equation using quadratic formula?Only a factorable quadratic expression can be solved using the factoring approach, and a quadratic equation with real roots can be solved using the graphing method, etc. However, the quadratic formula can be used to solve any kind of quadratic problem and gets over all these restrictions. step 1: Get into the standard form as the first step.step 2: Determine the values of a, b, and c by comparing the equation to [tex]ax^{2} +bx+c=0[/tex]Step 3: Replace the numbers in the quadratic equation, which is written as[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex] step 4: simplifyCalculation
by using the quadratic formula
[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]
where, a = 0.15, b = -39 and c = 4500
x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]
Hence, 130 units should be manufactured to minimize the cost of fax machines
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130 units should be manufactured to minimize the cost.
How to solve a quadratic equation using quadratic formula?Only a factorable quadratic expression can be solved using the factoring approach, and a quadratic equation with real roots can be solved using the graphing method, etc. However, the quadratic formula can be used to solve any kind of quadratic problem and gets over all these restrictions. step 1: Get into the standard form as the first step.step 2: Determine the values of a, b, and c by comparing the equation to [tex]ax^{2} +bx+c=0[/tex]Step 3: Replace the numbers in the quadratic equation, which is written as[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex] step 4: simplifyCalculation
by using the quadratic formula
[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]
where, a = 0.15, b = -39 and c = 4500
x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]
Hence, 130 units should be manufactured to minimize the cost of fax machines
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Write an equation in standard form of the line that passes through (-4,1) and has the slope m=3
An equation in standard form is ____ = -13
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y -1= 3 (x +4) \\\\\\ y-1=3x+12\implies y=3x+13\implies -3x+y=13\implies \boxed{3x-y=-13}[/tex]
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Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
1. Dianely's salary can be represented with the following table of values for 5 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
5 $50,000
2. The equation to model Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement equating two or more mathematical expressions.
Equations use variables, numbers, mathematical operands, and the equation symbol (=).
Dianely's initial salary = $40,000
Salary raise per year = $2,500
Dianely's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
5 $50,000 ($47,500 + 2,500)
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A new cruise ship line has just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the
Mediterranean Paradise. The Caribbean Paradise has 23 more deluxe staterooms than the Pacific Paradise. The
Mediterranean Paradise has 30 fewer deluxe staterooms than three times the number of deluxe staterooms on the
Pacific Paradise. Find the number of deluxe staterooms for each of the ships if the total number of deluxe staterooms
for the three ships is 518.
Answer:
Mediterranean Paradise has 30 fewer deluxe staterooms than three times the number of deluxe staterooms on the
Pacific Paradise.
Step-by-step explanation: