Answer:
f(2) = 0 and f(6) = -4
Step-by-step explanation:
First, find f(x) when x = 2
Plug in 2 as x in the function:
f(x) = -(x - 2)
f(2) = -(2 - 2)
f(2) = -(0)
f(2) = 0
Next, find f(x) when x = 6. Plug in 6 as x in the function:
f(x) = -(x - 2)
f(6) = -(6 - 2)
f(6) = -(4)
f(6) = -4
So, f(2) = 0 and f(6) = -4
hello i need help with my homeowkr math today please.
Given points A (1, 5) and B (-7, -5), which of the following coordinates is the midpoint of AB? (-3, 0) (-4, 0) (-2, 0) (4, 0) (2, 0)
The midpoint of the points A (1, 5) and B (-7, -5) is found to be (-3, 0)
What is midpoint of a line?The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.
How to find midpoint of a line segmentThe formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
Given points A (1, 5) and B (-7, -5)
X= (1 - 7)/2 = -3
Y = (5 - 5)/2 = 0
the midpoint is (-3, 0)
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Which of the following rational functions is graphed below?
On solving the question, we can say that second function has vertical asymptote at x=2
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.
The function that represents the graph is f(x) = 1/x-2 .
The graph of the function
From the given graph , the vertical asymptote is at x=2
Lets find out the vertical asymptote of each function
To find out vertical asymptote we set the denominator =0
f(x) = 1/2x
2x = 0
x = 0
f(x) = 1/x-2
x-2 = 0
x = 2
The second function has vertical asymptote at x=2
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From 4:00 to 5:00 p.m., the temperature dropped 6 °F. At 5:00 pm the temperature was 18°F. What was the temperature at 4:00 p.m.?
How do you Graph Y=1/2x-4
Answer:
To graph the equation y = 1/2x - 4, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
In this equation, the slope is 1/2, and the y-intercept is -4. The slope represents the steepness of the line, and the y-intercept is the point at which the line crosses the y-axis.
To graph the equation:
Plot the y-intercept, which is (-0, -4)
Using the slope, we can pick a second point on the line. The slope of 1/2 tells us that for every 2 units in the x direction, we will move 1 unit in the y direction. So we can pick a point that is 2 units to the right of the y-intercept, such as (2,0).
Connect the two points to get a straight line
The resulting graph will be a straight line that passes through the point (-0, -4) and (2, 0) and continues in both directions.
Alternatively, you can use a table of values to plot the points that belongs to the line and connect them, for example:
x | y
-2 | -5
-1 | -4.5
0 | -4
1 | -3.5
2 | -3
These are few points on the graph and with more points you can connect them and see the shape of the graph.
Step-by-step explanation:
Francis buys a package of 450 plastic forks. He uses 315 of the plastic forks.
What percent of the plastic forks did Francis use? Show your work.
Francis purchases a package of 450 plastic forks but only uses 315 of them, therefore he uses 70% of the available supply.
what is percentage ?In math, a % is a number or ratio that is expressed as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," and "pc." However, the percent sign "%" is frequently used to indicate it. The percentages' total quantity has no dimensions. Percentages are fundamentally fractions when the denominator is 100. Put a percent sign (%) next to a number to indicate that it is a percentage. For instance, if you successfully answer 75 out of 100 questions on a test (75/100), you get a 75%. Divide the money by the total to get percentages, then multiply the resulting number by 100. The formula (value/total) x 100% is used to calculate the percentage.
given
Francis purchases 450 plastic forks and
utilizes 315 of them, for
a percentage of 315/450*100
= 70%.
Francis purchases a package of 450 plastic forks but only uses 315 of them, therefore he uses 70% of the available supply.
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Consider the piecewise-defined function given by the graph. What are these values?
f(–3) =
f(–1) =
f(3) =
f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.
What are straight-line equations?
The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).
The variables x and y are related to coordinates on the line in the linear equation y = mx + c.
The formula y = mx + c yields a result for y when we enter a value for x.
As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.
According to our question-
m (x-x1) = y-y1 or
y = mx + c
Where,
Straight-line gradient, or m, is the line's slope.
The Cartesian coordinate that the line crosses is x1, y1.
the constant c
The calculation of the gradient (m) between any two locations on a line
m = Δy / Δx
f (-1) = Because x = -1, the function used is
y = 2, so f (-1) = 2 C) f (-3) = Because -3 -1,
the function used is y = -x-4, so f (-3) = - (- 3) -4 f (-3) = 3-4 f (-3) = -1 f (3) Since the function employed is
= -2x + 11 and x = 3, f (3) = -2 (3) +11, f (3) = -6 + 11, and f (3) = 5.
Hence, f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.
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Answer:-1
2
5
Step-by-step explanation:
simple answer
NO LINKS!!! Part 3
Find an exponential function y = ab^x form that satisfies the given information
f. passes through (-1, 72.73) and (3, 106.48)
g. passes through (-2, 351.56225) and (3, 115.2)
h. passes through (4, 405) and (9, 98415)
Answer:
[tex]\text{f)} \quad y=80(1.1)^x[/tex]
[tex]\text{g)} \quad y=225(0.8)^x[/tex]
[tex]\text{h)} \quad y=5(3)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Part (f)Given points:
(-1, 72.73)(3, 106.48)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 72.73=ab^{-1}[/tex]
[tex]\implies 106.48=ab^3[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{106.48}{72.73}=\dfrac{ab^3}{ab^{-1}}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=\dfrac{b^3}{b^{-1}}[/tex]
Solve for b:
[tex]\implies \dfrac{106.48}{72.73}=b^3 \cdot b^{1}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=b^{3+1}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=b^4[/tex]
[tex]\implies b=1.09998968...[/tex]
[tex]\implies b=1.1[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 72.73=a \cdot (1.09998968...)^{-1}[/tex]
[tex]\implies a=80.0022499...[/tex]
[tex]\implies a=80[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=80(1.1)^x[/tex]
---------------------------------------------------------------------------------------
Part (g)Given points:
(-2, 351.56225)(3, 115.2)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 351.56225=ab^{-2}[/tex]
[tex]\implies 115.2=ab^3[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{ab^3}{ab^{-2}}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{b^3}{b^{-2}}[/tex]
Solve for b:
[tex]\implies\dfrac{115.2}{351.56225}=b^3 \cdot b^{2}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=b^{3+2}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=b^5[/tex]
[tex]\implies b=0.800000113...[/tex]
[tex]\implies b=0.8[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 115.2=a(0.800000113...)^3[/tex]
[tex]\implies a=224.999904[/tex]
[tex]\implies a=225[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=225(0.8)^x[/tex]
---------------------------------------------------------------------------------------
Part (h)Given points:
(4, 405)(9, 98415)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 405=ab^4[/tex]
[tex]\implies 98415=ab^9[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{98415}{405}=\dfrac{ab^9}{ab^4}[/tex]
[tex]\implies 243=\dfrac{b^9}{b^4}[/tex]
Solve for b:
[tex]\implies 243=b^9 \cdot b^{-4}[/tex]
[tex]\implies 243=b^{9-4}[/tex]
[tex]\implies 243=b^{5}[/tex]
[tex]\implies b=3[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 405=a \cdot 3^4[/tex]
[tex]\implies 81a=405[/tex]
[tex]\implies a=5[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=5(3)^x[/tex]
I need help with this!!! What is the y intercept?
What is the equation of the line that passes through the points (10, 10) and (-2,-5)? Write your answer in slope-intercept form.
it's too late for this nonsense-
Given this equation...
4x - 1 6
--------- = -----
3x + 7 5
What is the value of x in this
proportion?
Answer:
x=91
Step-by-step explanation:
Follow the steps in the image.
add 16 to both sides
subtract 3 from both sides
divide by 1x
Plug answer back into equation
-Hope this helped
Need this answer please
Answer:
P = 5x + 33 = 58
Q = R = 3x+46 = 61
Step-by-step explanation:
angles in a triangle add up to 180 degrees
the angles in an isosceles triangle that correspond to the two congruent sides (are opposite the sides) are also congruent
that means that angle R = angle Q because QP and RP are congruent
angles = 5x+33, 3x+46, 3x+46
5x+33 + 3x+ 46 + 3x+46 = 180
11x + 125 = 180
subtract 125 from both sides to isolate the x and its coefficient
11x = 55
divide both sides by 11 to find x
x = 5
P = 5x + 33 = 58
Q = R = 3x+46 = 61
9. How many solutions does this system have? (1 point)
x-2y = 2
y=-2x+5
O infinitely many solutions.
Ono solutions
Otwo solutions.
one solution
The final statement is: The system of equations have unique solution.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: x-2y = 2 & y=-2x+5
Solving these two equations by method of substitution we get
x-2(-2x+5)=2
x+4x-10=2
5x=12
x=2.4
∴ y=2×2.4+5
=4.8+5
=9.8
Hence, The system has one solution.
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The point R(3, 3) is rotated 180 clockwise around the origin. what are the coordinates of the resulting point, R
help im almost out of time
The domain and the range of this function shown in the graph include the following;
B. Domain: all real numbers.
Range = f(x) ≥ -11
How to identify the domain and range of this graph?In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of this function (see attachment), we can reasonably and logically deduce the following domain and range:
Domain = -∞ ≤ x ≤ ∞ or all real numbers.
Range = f(x) ≥ -11 or [-11, ∞].
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Which expression is represented by the model?
The provided model represents the expression 4x-3.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.
Here,
You have 4 x's, then you minus 3,
=4x-3
The expression is represented by the model given is 4x-3.
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Nick has a checking account with the Park Slope Savings Bank. He writes both paper and electronic checks. For each transaction Nick enters the necessary information: check number, data, type of transaction, and amount. He uses E to indicate an electronic transaction. Determine the balance in his account after the Star Cable Co. check is written.
there is not enough information here to complete the problem.
f(x)=6-1/2x, h(x)=4(x-3)^2 Write f(h(x)) as an expression in terms of x
f(h(x)) = -2x^2 + 12x + (-12) in terms of x.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
To find f(h(x)), we first need to substitute h(x) into f(x).
f(h(x)) = f(4(x-3)²)
Now we can substitute 4(x-3)^2 into f(x)
f(h(x)) = 6 - 1/2(4(x-3)^2)
= 6 - 2(x-3)^2
= 6 - 2(x^2 - 6x + 9)
= 6 - 2x^2 + 12x - 18
Hence, f(h(x)) = -2x^2 + 12x + (-12) in terms of x.
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The average temperature for a country during September 2013 was 58.1 degrees Farenheit. This is 5.6 degrees Farenheit above the 20th-century average temperature for September. What was the country's 20th-century average temperature for September
Answer:
52.5
Step-by-step explanation:
58.1 - 5.6= 52.5
Solve for u
23= -8u-7+2u
Answer:
u = -5
Step-by-step explanation:
Isolate the variable, u. Note the equal sign, what you do to one side, you do to the other.
First, combine like terms. Like terms are terms that have the same amount of the same variables:
23 = -8u - 7 + 2u
23 = (-8u + 2u) - 7
23 = -6u - 7
Next, isolate the variable, u. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponsnts (& Roots)
Multiplications
Divisions
Additions
Subtraction
~
First, add 7 to both sides of the equation:
23 = -6u - 7
23 (+7) = -6u - 7 (+7)
23 + 7 = -6u
30 = -6u
Next, divide -6 from both sides of the equation:
-6u = 30
(-6u)/-6 = (30)/-6
u = 30/-6
u = -5
u = -5 is your answer.
~
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Answer:
[tex]u=-5[/tex]Step-by-step explanation:
[tex]23= -8u-7+2u[/tex]
[tex]-8u-7+2u=23[/tex]
[tex]-8u+2u-7=23[/tex]
[tex]-6u-7=23[/tex]
[tex]-6x-7+7=23+7[/tex]
[tex]-6u=30[/tex]
[tex]\cfrac{-6u}{-6}=\cfrac{30}{-6}[/tex]
[tex]u=-5[/tex]
Let u = [ 14 -1] and v= [14 1] show that [h k] is in span {u,v} for all and k
How can it be shown that a vector b is in Span {u,v}? O A. Determine if the system containing u, v, and b is consistent. If the system is inconsistent, then bis in Span{u,v}. O B. Determine if the system containing u, v, and b is consistent. If the system is consistent, b might be in Span {u,V}. C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then bis in Span{u,v}. O D. Determine if the system containing u, v, and b is consistent.
C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span{u,v} is correct.
To show that a vector b is in Span{u,v}, one way is to determine if it can be written as a linear combination of the vectors in the set, i.e., if there exist scalars h and k such that b = hu + kv. If this is the case, the system containing the equations hu + kv = b is consistent, meaning that there exist values of h and k that make the equation true. Therefore, if the system is consistent, it can be concluded that the vector b is in Span{u,v}.
Therefore, option C is the correct answer.
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What is the input for the function f(x)=4x-9 if the output is 11
Answer:
Input = 5
Step-by-step explanation:
Output = Answer a.k.a. f(x)
Input = x
We start by replacing f(x) with the output, which is 11
11 = 4x-9. I like making it opposite. It's easier in my eyes.
Making it opposite it's 4x-9 = 11
Now we need to get x by itself. The opposite of -9 is +9. So if we add 9 to each side, it deletes the 9 from the left and puts it on the other side, making it;
4x = 11 + 9. 11 + 9 is 20, so....
4x = 20.
Now 4x is the same as 4 times x. The opposite of times is divide. So let's divide by 4 on both sides. That gets rid of the 4 on the left side and puts it on the other side, making it;
x = 20/4. 20/4 is 5, so...
x = 5
Step-by-step explanation:
f(x) = 4x - 9
4x - 9 = 11
4x = 11 + 9
4x = 20
x = 20 ÷ 4
x = 5
a single line divides a plane into two regions. two lines (by crossing) can divide a plane into four regions; three lines can divide it into seven regions. let pn be the maximum number of regions into which n lines divide a plane, where n is a positive integer recurrence formula
The P(n) represents the maximum no of regions into which n lines divide the plain then P(k) = P(k-1) + k. (b). The formula for P(n) is [tex]1+{ }^{n+1} c_2\end{aligned}$[/tex]. (c). The 5152 regions can divide the plane for 100 lines.
When no. lines are drawn, we get one plain region.
Let the number of regions when divided by lines be represented by
P(0), P(1), P(2), P(3), P(n)
Therefore P(0) = 1
P(1) = 2
P(1) = P(0) + 1
P(2) = P(1) + 2
P(3) = P(2) + 3
P(4) = P(3) + 4………………….
P(n) = P(n-1) + n
Therefore, if P(n) represents the maximum no. of regions into which n lines divide the plain
Then P(k) = P(k-1) + k
(b).
⇒ P(0) = 1
⇒P(n) = P(n-1) + n
= P(n-2) + (n-1)+n
= P(n-3) + (n-2) +(n-1)+n……..
= P(0) + 1 + 2+ 4=3 + 4 + 5 +……+n
= P(0) + (Sum of the first n natural numbers)
[tex]$$\begin{aligned}& =P(0)+\frac{n(n+1)}{2} \\& =1+{ }^{n+1} c_2\end{aligned}$$[/tex]
Therefore, the formula for P(n) is [tex]1+{ }^{n+1} c_2\end{aligned}$[/tex].
(c)
Compute the value for n=100
[tex]$$1+{ }^{n+1} c_2=1+{ }^{101} c_2=1+\frac{101 \times 102}{2}=5152$$[/tex]
Therefore, the 5152 regions can divide the plane for 100 lines.
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A single line divides the plane into two regions. Two lines (by crossing) can divide the plane into four regions; three lines can divide it into seven regions, etc. Let P(n) be the maximum number of regions into which n lines divide a plane, where n is a positive integer.
(a) Derive a recurrence relation for P(k) in terms of P(k-1) for all integers [tex]$k \geq 2$[/tex].
(b) Use iteration to find an explicit (closed) formula for P(n).
(c) Into how many regions can 100 lines divide the plane?
Please solve this ill mark brainlest please actually asnwer no answer = report
Answer:
Step-by-step explanation:
∠ADB=360-90=270°
circumference of circle=2πr=2π×3=6π m
length of arc ADB
[tex]=\frac{270}{360} \times 6\pi \\=\frac{3}{4} \times 6\pi \\=\frac{9}{2} \pi \\\approx 14.137~m\\[/tex]
area of circle =πr²=π×3²=9π m²
area of shaded region
[tex]=\frac{270}{360} \times 9\pi \\=\frac{27}{4} \pi ~m^{2} \\\approx 21.206~m^2[/tex]
how many groups of 1/5 are in 4
Answer: 20
Step-by-step explanation: Since it is 1/5 you multiply the 5 by 4 and get 20.
Answer:
20
Step-by-step explanation:
It is 20 because you have to multiply the denominator by the whole number.
Someone help please!! I only need the questions that are circled.
Answer:
Question 8: (-4,7)
Question 10: (5,2)
Step-by-step explanation:
What are equations?:
Two mathematical expressions are equal.⇒ Example; 2x + 5 = 25 is an equation, in which 2x + 5 and 25 are two expressions separated by an equal (=) sign.What is Substitution Method?:
The value of one variable from one equation is substituted in the other equation.y = -2x - 1
3x - 4y = -40
Question 8:
3x - 4(-2x-1) = -40
3x + 8x + 4 = -40
11x + 4 = -40
11x = -44
x = -4
To find y we can substitute x into the equation.
y = -2(-4) -1
y = 8 -1
y = 7
(-4,7)
Question 8 Solution - (-4,7)
Question 10:
2x - y = 8
x = 5
Since this equation already given x we can substitution to find y.
2(5) - y = 8
10 - y = 8
-y = -2
y = 2
(5,2)
Question 10 Solution - (5,2)
Lenvy~
can someone help me with these 2 Images, please? it's for geometry
Question 1
[tex]11+2x+29=x+28 \\ \\ 2x+40=x+28 \\ \\ x+40=28 \\ \\ x=-12[/tex]
Question 2
A, B, E
Y=(x-2)^2+3 vertex form to standard form
The required vertex form of the given equation is y = x² - 4x + 7.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
y = (x - 2)² + 3
Simplifying the expression,
y = x² -4x + 4 + 3 {since (a - b)² = a² + b² -2ab}
y = x² - 4x + 7
Thus, the required vertex form of the given equation is y = x² - 4x + 7.
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Write an equation that represents the line.
Use exact numbers.
Answer:
-5x+5
Step-by-step explanation:
That would be the answer
there are 36 eggs in a crate if 24 are fried what percentage is left
Answer:
33.33%
Step-by-step explanation:
You start with 36 eggs, and 24 are removed and fried. This means that the remaining eggs are the difference of 36 and 24:
36 - 24 = 12
There are 12 eggs left! To find the percentage of remaining eggs, write a ratio comparing the number of eggs that remain to the original amount of eggs:
[tex]\frac{12}{36}[/tex]
Now, simplify the fraction into a decimal:
12 ÷ 36 = 0.3333...
Multiply a decimal by 100 to convert it to a percentage:
0.3333... ⋅ 100 = 33.33...%
Rounded to the nearest hundredth, the percent of remaining eggs is 33.33%