Answer:
1 - 5 < y < 5
I hope you pass your assignment
The range of solutions for the given inequality is -5<y<5.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -6<1/3(6y + 12)<14.
Here, -6<(2y + 4)<14
-6<(2y + 4)
Subtract 4 on both the sides of an inequality, we get
-10<2y
Divide 2 on both the sides of an inequality, we get
-5<y
(2y + 4)<14
Subtract 4 on both the sides of an inequality, we get
2y<10
Divide 2 on both the sides of an inequality, we get
y<5
So, -5<y<5
Therefore, the range of solutions for the given inequality is -5<y<5.
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5. The population of a town went from
100,000 to 137,000 in 5 years. What was
the percent increase in the town's
population
over that time?
A 7.4%
B 37%
C 73%
D 137%
Answer:B or A depending on if it went per year or overall
Step-by-step explanation:100 137, 137-100=37
37/5=7.4
Evaluate the integral by reversing the order of integration.
2
0
6
11ex2 dx dy
3y
When we reverse the integration and evaluation orders, we obtain: [tex]\frac{c}{2}-1[/tex]
What is integration?In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
So, we have:
[tex]$$\int_0^1 \int_x^z e^{\frac{x}{y}} d y d x$$\\[/tex]
Here: [tex]z=\sqrt{x}[/tex]
Next, reverse the sequence:
[tex]$$\int_0^1 \int_m^y e^{\frac{x}{y}} d y d x$$ $m=y^2$$$\\\\\begin{aligned}\\& \int_{=0}^1\left(e^{\frac{x}{y}} y\right) \| \begin{array}{l}y \\y^2\end{array} d y \\& \int_{=0}^1(e y)-\left(e^y y\right) d y\end{aligned}$$[/tex]
The following section uses integration by parts,
[tex]$$\begin{aligned}& \mathbf{u}=\mathbf{y}, \\& d v=e^y\end{aligned}$$$$\mathrm{d} u=1$$$$v=e^y$$$$\begin{aligned}& =\left(\left(\frac{e y^2}{2}\right)-\left(y e^y\right)\right)||_0^1+\int_0^1 e^y d y \\& = \\& =\frac{e}{2}-e+e-1=\frac{e}{2}-1\end{aligned}$$[/tex]
Therefore, when we reverse the integration and evaluation orders, we obtain: [tex]\frac{c}{2}-1[/tex]
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Correct question:
Evaluate the integral by reversing the order of integration.
8 0 2 3ex4 dx dy 3 y
Making connections between arithmetic sequences and linear function
Use the graph or the formula to write the equation of the line in a slope intercept form
On solving the provided question, we can say that - here in graph we have on solving equation [tex]x^2+ 3y^2 \\[/tex] = [tex]4+3 = 7[/tex]
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here-
from graph, x= 2
y = 1
[tex]x^2+ 3y^2 \\[/tex]
[tex]4+3 = 7[/tex]
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For each condition, make up a different equation for a quadratic function that meets the condition. Use whatever form is most conventions.
1. Has vertex at (-2,-5)
2. Has a y-intercept at (0,6)
3. Goes through the points (4,2) and (1,2)
y=−12(x+4)(x−1) A quadratic function that satisfies the requirement and passes through the points (4, 2) and has the equation +2 (1,2) .
what is equation ?A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.
given
a )a vertex at (−2,−5) :
y=[tex](x+2)^{2}[/tex]−5
y=−[tex](x+2)^{2}[/tex]−5
y=3[tex](x+2)^{2}[/tex]−5
b) a y-intercept of (0,−6) :
y=[tex]x^{2}[/tex]−6
y=[tex]x^{2}[/tex]+13x−6
y=2[tex]x^{2}[/tex]−6
c) the points (−4,2) and (1,2):
y=(x+4)(x−1)+2
y=2(x+4)(x−1)+2
y=−12(x+4)(x−1)+2
y=−12(x+4)(x−1) A quadratic function that satisfies the requirement and passes through the points (4, 2) and has the equation +2 (1,2).
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Susan earns $10 per hour tutoring elementary students in math. She also earns $15 per
hour cleaning in the library. Her goal each week is to earn at least $240 while working no
more than 20 hours.
Let e represent the number of hours Susan works in one week tutoring elementary students,
and let c represent the number of hours Susan works in one week cleaning the library.
Which inequalities represent Susan's weekly goal of earning money?
Inequalities represent Susan's weekly goal of earning money are:
c + e ≤ 20
15c + 10e ≥ 240
What is an inequality?The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.
The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.
Given that,
Susan earns $10 per hour tutoring elementary students in math.
She also earns $15 per hour cleaning in the library.
Her goal each week is to earn at least $240 while working not more than 20 hours.
Thus, the equation of inequality:
c + e ≤ 20
15c + 10e ≥ 240
Here, e represent the number of hours Susan works in one week tutoring elementary students.
c represent the number of hours Susan works in one week cleaning the library.
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[need some help! will give brainlist!]
Write the terms in standard form. Then state the degree of the polynomial and the leading coefficient (LC).
It can be written in standard form as [tex]5x^2-2+3[/tex] and the degree of polynomial is 2 with leading coefficient as 2.5.
How do you format a standard form of writing?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). When attempting to solve systems of two linear equations, this form is also very helpful.
What are some terms examples?The values on which mathematical operations take place in an algebraic expression are known as terms in mathematics. Let's explain with the help of a term example. This algebraic expression has terms 8x and 9, respectively.
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PLEASE ANSWER ASAP WILL GIVE BRAINLIEST
Answer:
Translate(1.3, -1)
Scale Factor: 2/3
Step-by-step explanation:
First, perform a dilation about the origin. This will make the original shape smaller.
From the given diagram, we can see that R'S' is 10 units long. RS is 15 units long. Using this information, we can create this ratio.
[tex]\frac{10}{15}[/tex]
This means that Triangle R'S'T' is 2/3 of Triangle RST. Construct lines from the origin (the center of dilation) to each point on the original triangle. Then, find two thirds of that line. The new point will be the new y-coordinate.
The new coordinates will (approx.) be:
R = (-2, 4.7)
S = (-2, -5.3)
Only two coordinates are necessary to perform this translation. As per the graph, this triangle must shift approximately 1.3 units up and 1 unit to the left. Thus, the final translation is:
Translate(1.3, -1)
Scale Factor: 2/3
pls help me on this question
1) false
2) false
3) true
4) true
5) true
Answer:
1 false,2 false,3 true,4 true,5 true
What is the sum of 1.3 and –1.8?
Answer in explanation:
although there's an addition sign, you subtract the two because a
(+) + (-) = (-) subtract
[This is a general rule, writing down the "rules" for reference is a good way to help if your having trouble]
subtract to find your answer (you keep the sign of 1.8 because it's the larger number.)
1.3 + (-1.8) =
-0.5
-0.5 is your answer
Hope this is clear!
Can someone explain to me how to do this?
solve × ÷ - 2 = 7
x = ?
Answer: -14
Step-by-step explanation: When you have a problem like this all you do in multiply the answer and the number your given.
7x-2 that would by -14
You want to check your answer by changing X for -14 and you solve from there. Plus 2 negatives equal a positive.
Hope this helps!
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{x}{-2} = 7}[/tex]
[tex]\text{Multiply } \rm{ -2}\text{ to both sides}[/tex]
[tex]\mathsf{\dfrac{x}{-2}\times -2 = 7\times -2}[/tex]
[tex]\text{Simplify it}[/tex]
[tex]\mathsf{x = 7\times -2}[/tex]
[tex]\mathsf{x = -14}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = -14}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Assuming that birthdays are distributed equally throughout the week, what is the probability that two people that have never met passing each other on the street were both born on a Friday is
1/7 2/7 1/49 2/49 4/49
Probability of Two people was born on Friday = 1/49
What is the definition of probability?
Possibility of happening an event is called probability. It is given by the ratio of favorable outcome to the total possible outcome. Probability is different kinds such as independent probability, dependent probability, conditional probability and so on.
What is the probability that two people were born on a Friday?
Assume that birthdays are equally distributed throughout the week.
probability of one people having birthday on Friday = 1/ 7
probability of another people has birthday on Friday = 1/7
probability of two people was born on Friday = 1/7× 1/7 = 1/ 49
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Find the centre focus,vertex,directrix and axis of each parabola and sketch the graph? (x-1)² = y+2
The answers to each part of the question are mentioned above.
What is parabola?In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.The general equation of a parabola is given by -y = a(x – h)² + k or x = a(y – k)² +h.
where - (h, k) denotes the vertex.
Given is the equation of a parabola as -
(x - 1)² = y + 2
We can write the equation as -
y = (x - 1)² - 2
The coordinates of the vertex are : (h, k). So, we can write the coordinates of the vertex as V(1, - 2).The equation of a parabola is -[tex]$y=\frac{1}{4 \left(f - k\right)} \left(x - h\right)^{2} + k[/tex]
We can rewrite the equation of the parabola given as -[tex]$y=\frac{1}{4 \left(\frac{-7}{4} - (-2)\right)} \left(x - h\right)^{2} + k[/tex]
The coordinates of the focus are : (h, f). The coordinates of the focus will be - F(h, f) or F(1, -7/4)The distance from the focus to the vertex is the same as the distance from the vertex to the directrix so -- 2 - (- 7/4) = d - (- 2)
d = - 9/4
The equation of directrix will be :y = d
y = -9/4
The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: x = 1
Therefore, the answers to each part of the question are mentioned above.
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Is y 4 a horizontal asymptote?
Yes, the horizontal asymptote is at y = 4.
The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any infinite distance.
Here we have given the expression y = 4.
In order to find whether it is an horizontal asymptote or not, we have to plot it on the graph,
The first process is to label the graph with x and y axis.
And then we have to defines the scale for the for the graph.
Now, we have to input the expression y = 4 on the graph then we get the graph like the following.
While we looking into the given graph we have identified that the expression y = 4 makes the horizontal asymptote on the graph.
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The table shows the heights y (in centimeters) of a plant after x weeks. Use the table to complete the statements.
x 0
4
8
y 17 29 41
Coroline runs 3 1/2 miles in 22 1/4 minutes how many miles does she run per minute
Answer:
To determine the number of miles Coroline runs per minute, we need to first convert the distance she runs to a fraction of a mile and the time it takes her to run that distance to a fraction of an hour.
3 1/2 miles is equivalent to 3 + 1/2 = 3 + 1/(2*1) = 7/2 miles.
22 1/4 minutes is equivalent to 22 + 1/4 = 22 + 1/(4*1) = 23/4 minutes.
To convert the time to hours, we can divide the number of minutes by the number of minutes per hour. There are 60 minutes per hour, so we have:
23/4 minutes / (60 minutes/hour) = (23/4) / (60/4) = 23/60 hours
To determine the number of miles Coroline runs per minute, we can divide the distance she runs by the time it takes her to run that distance:
(7/2 miles) / (23/60 hours) = (7/2) / (23/60) = (760) / (223) = 420/46
Simplifying, we have:
420/46 = 9 1/23
Therefore, Coroline runs approximately 9 1/23 miles per minute.
Step-by-step explanation:
Answer:
she runs 0.078 miles per minute.
Step-by-step explanation:
Find the rate of change for this linear function.
y = 5x - 1
Find the initial value of the linear function
Y=5x+2
rate of change for this linear equation, y = 5x - 1 is +5
the initial value of the linear equation, y = 5x + 2 is +2.
What is linear equation?A linear equation is an algebraic equation of the form y = mx+c, where m is the slope and c is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." If a linear equation contains two variables, it is referred to as a linear equation in two variables, and so on.
Non-linear equations are those that do not produce a straight line. It has a changeable slope value and resembles a graphed curve.
Given that,
y = 5x - 1 is a linear equation.
As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.
Therefore, for the given equation, rate of change is 5 and initial value is -1.
Given that,
y = 5x + 2
is a linear equation.
As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.
Therefore, for the given equation, rate of change is 5 and initial value is + 2.
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Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. complete the diagram to show smaller and larger batches that would taste the same as lin's favorite blend. please
help it's due tomorrow
The ratios on the double line are 3:7, 6:14, 12:28 and 15:35.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line.
From the given double line, the ratio is 9:21.
Completed double line has the following ratios
3:7, 6:14, 12:28, 15:35
Therefore, the ratios on the double line are 3:7, 6:14, 12:28 and 15:35.
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50 points help me out
Answer:x=20
Step-by-step explanation: <2 and <3 must be equal, so set 3x-10 equal to x+30, once simplified you get x equal to 20.
Answer:
x = 20
Step-by-step explanation:
Angle 2 and 3 are alternate (interior) angles which means that they are equivalent to each other.
3x-10=x+30
-x -x
2x-10=30
+10 +10
2x=40
x=20
A line is parallel to y = -3x + 2 and
intersects the point (4, 3). What is the
equation of this parallel line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y₁ = m(x -x1)
Then write the equation in slope-intercept form.
Enter
Answer:
the equation of line parallel to y=-3x+2
is y=-3x+k---(1)
Since,line(1) passes through point (4,3).
3=-3(4)+k
or,3=-12+k
or,k=3+12
:.k=15
Putting value of k in line (1), we get
y=-3x+15,which is the required eqn.
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PLS HELP I HAVE NO IDEA
Complete the remainder of the table for the given function
y=x/2 + 5
Answer:
Step-by-step explanation:
(-2,4)
(0,5)
(2,6)
(4,7)
Answer: 4, 5, 6, 7,
Step-by-step explanation: From the formula y = x / 2 + 5
substitute x with the value -2
It becomes -2 / 2 + 5
that equals 4
then do the same for the rest
when x = 0
y = 0 / 2 + 5
y = 5
when x = 2
y = 2 / 2 + 5
y = 1 + 5
y = 6
when x = 4
y = 4 / 2 + 5
y = 2 + 5
y = 7
I hope this was helpful
Lin is solving the inequality 15-x< 14. She knows the solution to the
equation 15 - x = 14 is x = 1
How can Lin determine whether x > 1 or x < 1 is the solution to the
inequality?
If Lin is solving the inequality [tex]15-x < 14[/tex] and she know the solution is x = 1 , then the solution of inequality is [tex]x > 1[/tex] .
The inequality that Line is solving is [tex]15-x < 14[/tex] ,
the solution of the equation [tex]15-x = 14[/tex] is given as x = 1 ;
we have to find the value of x for which the given inequality expression is true ,
Case(i) , let us take [tex]x > 1[/tex] ,
So , putting x = 2 , in the inequality ,
we get ; [tex]15-2 < 14[/tex]
= 13 < 14 , that is TRUE .
Case(ii) , let us take [tex]x < 1[/tex] ,
So , putting x = 0 in the inequality ,
we get ; [tex]15-0 < 14[/tex]
= 15 < 14 , that is FALSE .
Therefore , the solution of the inequality is x > 1 .
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Let g be a twice-differentiable function with g'(x) > 0 and g"(x) > 0 for all real numbers x, such that
g(3) 12 and g(5) = 18. Which of 20, 21, and 22 are possible values for g(6) ?
(A) 21 only
(B) 22 only
(C) 20 and 21 only
(D) 21 and 22 only
g(6) must be greater than 21 which is 22 only.
What is function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable.
Since g'(x) > 0 for all x and we know that g(x) is an increasing function.
Additionally, since g"(x) > 0 for all x, we know that g(x) is a concave-up function.
Since g(x) is increasing, we know that g(6) > g(5) = 18.
Now, we can use the fact that g(x) is concave-up to find a lower bound on g(6).
By the definition of concave-up, we know that the slope of the tangent line to g(x) is increasing.
This means that the slope of the line connecting (3,g(3)) to (5,g(5)) is less than the slope of the line connecting (5,g(5)) to (6,g(6)).
Using this information, we can find a lower bound on g(6):
g(5)- g(3) / (5-3) < g(6)- g(5)/ (6-5)
18- 12/2 < g(6)- 18
3 < g(6) - 18
g(6) > 21
Therefore, g(6) must be greater than 21.
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please help i need help asap i have class in 2 hours pls
The value of x, given the angles next to the triangle, can be found to be 38 °
How to find the value of x ?To find the value of x, you first need to find the value of the other angles in the triangle.
Angles on a horizontal line add up to 180 degrees so the angle to the bottom left is:
= 180 - 134
= 46 °
The angle to the bottom right is:
= 180 - 84
= 96 °
The angles in a triangle add up to 180 ° so the value of x would be:
= 180 - 46 - 96
= 38 °
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The table shows pairs of values for the linear function f(x) = 3x
f(x)
-2
1
4
7
10
X
0
1
2
3
4
Which conjecture about linear functions in general is best supported by the
table?
Equal changes in the value of x
result in equal changes in the value
of y.
B. The difference between the x- ar
y-values in each ordered pair (x,
is a constant.
Answer:
the answer is. The answer is
57
Step-by-step explanation:
If the original price is 125 pesos and the rate of discount is 25%, how much is the discount? with solution
Answer:
31.25
Step-by-step explanation:
25% * 125 = 25/100 * 125 = 1/4 * 125 = 31.25
Find the area of the polygon with the given vertices.
W(-1, 1)
-4
Z(-3,-2)
4
Ay
2
-4
2
X(4,1)
4 x
Y(2,-2)
The area of a polygon with the given vertices is calculated by adding the areas of the individual triangles that make up the polygon.
What is polygon?A polygon is a closed figure in a plane consisting of a set of straight line segments connected end-to-end. The sides of a polygon are all of equal length, and the angles between them are all of equal measure. Polygons are one of the most fundamental shapes in geometry. They include triangles, squares, rectangles, hexagons, and many more.
The area of triangle WXZ is calculated as (1/2) × |XW × ZY|,
where XW is the vector from W to X and ZY is the vector from Z to Y.
In this example,
XW = (3, -2) and ZY = (-2, -4).
Therefore, the area of triangle
WXZ is (1/2) ×|(3, -2) × (-2, -4)| = (1/2) × 14 = 7.
The area of triangle XYA is calculated similarly,
where XY = (2, 3) and YA = (-2, -4).
Therefore, the area of triangle
XYA is (1/2) ×|(2, 3) ×(-2, -4)| = (1/2)× (-14) = -7.
The area of the polygon is calculated by adding the areas of the individual triangles, which in this example is 7 + (-7) = 0. Therefore, the area of the polygon with the given vertices is 0.
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.A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200
A: If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?
B: If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?
C: If the car spends no time going 35 miles per hour, how long would the trip take? Explain your reasoning.
Answer:
This equation can be used to determine how long the car was traveling at each speed. You can solve for one of the variables by using algebraic techniques. For example, you could subtract 35y from both sides to get:
55x = 200 - 35y
Then divide both sides by 55 to get:
x = (200 - 35y)/55
This equation shows that the value of x (the time spent traveling at 55 mph) is determined by the value of y (the time spent traveling at 35 mph). If you know the value of y, you can use this equation to calculate the value of x.
To find the values of x and y that satisfy the equation, you will need to use additional information. For example, you could set up a system of equations and solve for x and y using techniques such as substitution or elimination.
Step-by-step explanation:
If ABCD is dilated by a factor of the
coordinate of D' would be:
4-3
12
3
N
18
T
2
3
4
5
O
9 10
D'=([?]))
Enter
When ABCD is dilated by a factor of the coordinate of D' and the size of the coordinate point is, A"s coordinate would be (-6, -2) (-3, -1) .
what is coordinates ?When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.
given
The coordinate point's size is specified as (-3, -1).
The coordinate A' will be supplied as follows if the coordinate A is dilatable by a factor of two: A' = (2(-3), 2(-1)) = (-6, -2)
Consequently, A"s coordinate would be (-6, -2)
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pls solve me this functions question
On solving the provided question, we can say that - the value of the function is f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]; f(x) = x= it doesn't factor
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
f(x) = [tex](x+3)^2 - 5[/tex]
f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]
f(x) = x= it doesn't factor
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What it means when a function and its inverse is the same?
Step-by-step explanation:
it means that the graph of the function above y=x must be the mirrored image of the graph under y=x.
it means that the function applied to itself gives x.
f(f(x)) = x
e.g.
f(x) = 5 - x
f(f(x)) = 5 - (5 - x) = 5 - 5 + x = x
so, this f(x) is its own inverse.