Answer:
[tex]g(x) = \frac{6}{5}x + 8[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 6x + 8[/tex]
[tex]k = 5[/tex] --- horizontal stretch factor
Required
Find g(x)
When a function is stretched horizontally by k, the resulting function will be:
Rule: [tex]g(x) = f(\frac{1}{k}x)[/tex]
So, we have:
[tex]g(x) = f(\frac{1}{5}x)[/tex]
Solve for: [tex]f(\frac{1}{5}x)[/tex]
[tex]f(\frac{1}{5}x) = 6 * \frac{1}{5}x + 8[/tex]
[tex]f(\frac{1}{5}x) = \frac{6}{5}x + 8[/tex]
Recall that:
[tex]g(x) = f(\frac{1}{5}x)[/tex]
[tex]g(x) = \frac{6}{5}x + 8[/tex]
Answer:
f(1/5x) = 6 ^1/5x +8
Step-by-step explanation:
A horizontal stretch by a factor of 5 means that the input, or x, is multiplied by : 1/5
What is the formula for the volume V of a cylinder with base area B and height H?
The formula for the volume of cylinder with base area B and height H is V = B × H.
What is the volume of the cylinder?A cylinder is a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Area of a circle which is the base of a cylinder = πr²
Given that;
Base area = BHeight = HPlug the given values into the above formula.
V = π × r² × h
V = πr² × h
V = Base area × Height
V = B × H
Therefore, formula for the volume is V = B × H.
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Find [g ο f](-4) given f(x) = x + 4 and g(x) = -2x2
Answer:
Step-by-step explanation:
(
1
)
.
plugging the
4
into
g
(
x
)
and then putting what you get from that in to
f
(
x
)
(
2
)
.
plug
g
(
x
)
into
f
(
x
)
and then plug in the
4
Option 1:
Plug
4
into
g
(
x
)
:
g
(
x
)
=
−
2
(
4
)
−
6
=
−
8
−
6
=
−
14
Then plug
g
(
x
)
into
f
(
x
)
:
f
(
x
)
=
3
(
−
14
)
−
7
=
−
42
−
7
=
−
49
Option 2:
Plug
g
(
x
)
into
f
(
x
)
:
f
(
x
)
=
3
(
−
2
x
−
6
)
−
7
=
−
6
x
−
18
−
7
=
−
6
x
−
25
Finally plug
4
into our current
f
(
x
)
:
f
(
x
)
=
−
6
(
4
)
−
25
=
−
24
−
25
=
−
49
How do you find the degree and the number of turning points in a polynomial function?
To find the degree of a polynomial function, count the number of terms in the expression. To find the number of turning points, take the degree of the polynomial and subtract 1. The number of turning points will be equal to that number.
To find the degree of a polynomial function, the first step is to count the number of terms in the expression. For example, if the expression is 3x^2 + 4x + 2, then the degree is 2 because there are three terms.The second step is to subtract 1 from the degree of the polynomial. In the example, subtracting 1 from 2 gives us 1. Therefore, the polynomial has 1 turning point.A turning point is a point on the graph of the polynomial where the slope of the tangent line is 0. This means the graph changes direction at the turning point. In the example, the graph changes direction at the point (1, 5).In summary, to find the degree and the number of turning points in a polynomial function, count the number of terms in the expression to find the degree, then subtract 1 from the degree to find the number of turning points.
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a sailing ship stopped at several islands, releasing one mating pair of goats onto each one. on the smallest island, the limited food supply could only support a total of 1500 goats. if their per capita growth rate is 0.5 per year, how many years will it take before the goat population on the smallest island reaches 1000?
After 6 years the population of goats on the small island reaches 1000.
What is per capita growth rate?It is the rate of increases of population per individual in the population. The term related to time period and entire population.
How to calculate the time to reach the maximum populationgiven, initial population of goat on the smallest island, N° =2,
after t years the population of goats on this island, N= 1000
the maximum goat carrying capacity of this island, K= 1500
per capita growth rate, r = 0.5 per year
now, we use logistic growth equation, dN/dt = r×N[(K-N)/K]
dN/dt = 0.5×1000{1500-1000)/1500}
dN/dt= 166.67
∫dN/166.67 = ∫dt
by integrating both sides
N/166.67 = t+c , where c is the
integration constant
at time t=0, N°=2
c= 0.012
N/166.67 =t+0.12
as N=1000 , t= 5.99 years
hence, after 6 years the population of goat on the island reaches 1000.
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The width of a rectangle is the length minus 5 units. The area of the rectangle is 14
units. What is the width, in units, of the rectangle?
The width of the rectangle is 2 units.
What is the width of a rectangle?Despite having four sides, a rectangle only has two distinct dimensions since the sides are paired. Though the width is often the shorter of these two dimensions, it is more commonly referred to as the horizontal side when the rectangle is shown lying on its side.
Calculation:Given the width of rectangle is length of rectangle - 5 units.
Let us suppose that length of rectangle is y and width of the rectange is y-5.
The formula of area of rectangle is l×b where l and b are length and breadth respectively.
So substituting in the equation we get
[tex]y* (y-5) = 14.\\y^2- 5y = 14\\y^2 - 5y - 14 = 0[/tex]
Solving the above quadratic equation we get y as 7 and -2.
As length cannot be a negative quantity we take length as 7 and it gives us the result that the width is 2 units.
The width of the rectangle is 2 units.
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How do you find the vertical and horizontal asymptotes of a function using limits?
To find the vertical asymptote, take the limit of the function as x approaches infinity or negative infinity. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain.
To find the vertical asymptote of a function, take the limit of the function as x approaches either infinity or negative infinity. This will give the value at which the output of the function approaches infinity or negative infinity, respectively. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain. If the limit of the function as x approaches the endpoint is finite, then the horizontal asymptote is the value of the limit. If the limit of the function as x approaches the endpoint is infinite, then the horizontal asymptote is undefined. If the limit of the function as x approaches the endpoint is undefined, then the horizontal asymptote is undefined.
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In a series of transformations, which transformation would make two figures similar as opposed to congruent? answer choices.
a. translation
b. dilation.
c. reflection.
d. rotation.
If PS= RS = 31, PQ = 2v, and QR = v + 23, what is the value of v?
The value of the v is 11.5 units.
What is a Line Segment?
A line segment is a portion of a straight line that is defined by two points. It is a one-dimensional geometric figure with no width or area. Line segments can be drawn in many ways, including straight, curved, or jagged. The length of a line segment is the distance between the two points that define it. Line segments are commonly used to measure distances, form shapes, and construct geometric figures. Line segments can be used to define polygons, circles, and other shapes. Line segments are also used in mathematics to represent vectors and calculate angles. Line segments are a fundamental element of geometry and are used in a variety of applications, including navigation, construction, engineering, and computer graphics.
We have,
PS= RS = 31,
PQ = 2v,
and QR = v + 23,
v = ?
If PS= RS = 31,
then PQ = QR,
so, 2v = v + 23,
v = 23/2
v = 11.5 unit
Hence, the value of the v is 11.5 units.
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If 3x + 5y = 25, what is the value of 3x + 5y/5 =
Answer: 5
Step-by-step explanation: if you do something to one side of the equation, it has to be done to the other side.
in this case, they divided the left side (3x+5y) by 5
so so make both sides equal, you'd have to divide the right side (25) by 5 as well which would give you 5
What are the vertical and horizontal asymptotes of F x )= 3x 2 x 2 4?
As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.
What is vertical asymptote?On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).
What is horizontal asymptote?A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.
We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.
Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.
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Determine the range of the following graph:
Answer:
-1 ≤ y ≤ 6
Step-by-step explanation:
The range is the values of y.
In this graph lowest point is -1 and the highest is 6.
The points are filled so that means that we include 6 and -1.
So it would be -1 ≤ y ≤ 6.
Draw a line representing the 'rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
Rise and Run of line's ratio gives the Slope of the line.
What is rise of line and run of line?Rise of a line is the how many units you move up or down to reach from one point to another point. Run of a line is the how many units you move left or right to reach from one point to another.
>Slope of a line is the ratio of the rise to the run of the line.
Let us assume the graph of y = x.
Now in the graph we take three points
let point 1 be (3,3) = (x1,y1)
point 2 be (5,5)= (x2,y2)
point 3 be (5,3)= (x3,y3)
Now the rise is y2 - y1 which is 2
Now the run is x2 - x1 which is 2
Slope is [tex]\frac{rise}{run}[/tex] = [tex]\frac{2}{2} =1[/tex], we know that slope of line y=x is 1 and here we get the same so it is proved that slope of line is [tex]\frac{rise}{run}[/tex] .
Rise and Run of line's ratio gives the Slope of the line.
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PLS HELP!
The figure shows a loading dock and a side view of an attached ramp, whose run is 12 feet and whose rise is 39 in. Devyn is wondering whether a long rectangular box can be stored underneath the ramp, as suggested by the dotted lines. The box is 2ft tall and 5ft long. Answer Devyn's question.
With the help of Trigonometry the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.
What is Trigonometry?
Studying the correlations between triangle side lengths and angles is the subject of trigonometry, a branch of mathematics. From the use of geometry in astronomical research, the field first appeared in the Hellenistic world in the third century BC.
Dimensions are the measure of the length, width and height of a given object. Yes, a rectangular box of length 5 feet and height 2 feet can be stored underneath the ramp.
The measure of the sides of a given object is referred to as its dimensions. This can be with respect to its length, width, and height.
It has been given that the height of the ramp is 39 inches. But,
12 inches = 1 feet
So that,
39 inches = x feet
make x the subject of the formula to have;
x = 3.25 feet
Thus the dimensions of the ramp are ;
length = 12 feet
height = 3.25 feet
Therefore, the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.
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Question 67
Use substitution to solve the system of equations.
y=x+8
2x-3y=5
O (19,27)
O (-21, -29)
O (-29, -21)
O (-5,3)
What is the domain and range of f/x )= x³?
domains = all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value the minimum. The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
domains = all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)
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What is median class example?
The continuous data that is presented as a frequency distribution makes up the median of the grouped data.
The center number in the set of data, known as the median, is what divides the data set's upper and lower halves. Since the data is divided into class intervals, the middle value is unknown when calculating the median of grouped data.
Let us understand this with the help of a median class example.
Consider the data as 48, 20, 59, 69,73. We have to calculate the median.
Arranging in ascending order we get, 20, 48, 59, 69, 73.
Here the number of observations is n = 5.
To find the median of odd data we will use the formula:
[(n+1)/2] = (5+1)/2 = 3.
Therefore, median = 3rd observation.
Median = 59.
Hence we got the idea of the median with the example of class.
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What is the additive inverse of
Answer:
Subtraction
Step-by-step explanation:
The additive inverse of something will use subtraction, basically the opposite
An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 1300 meters, and Plane B was at an altitude of 1092 meters. Plane A is gaining altitude at 17 meters per second, and Plane B is gaining altitude at 21 meters per second. Let x be the number of seconds passed
(A) The expression for each plane are as follows;
Plane A; 1300 + 17x
Plane B; 1092 + 21x
B). The equation to show when the two planes would be at the same altitude is; 1300 + 17x = 1092 + 21x.
Which equation shows when the two planes would be at the same altitude?It follows from the task content that the initial altitudes of plane A and B are 1300 and 1092 respectively.
Since plane A gains altitude at 17 meters per second; The expression for the altitude after x seconds is;
1300 + 17x
Also, since plane B gains altitude at 21 meters per second; The expression for the altitude after x seconds is;
1092 + 21x
Ultimately, at the point when the two planes are at the same altitude; the equation which is true about the situation is;
1300 + 17x = 1092 + 21x.
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Which tool would you use to make chart?
The
tools
used to make a
chart
are Info-gram, tableau, Grafan, Chartist
What is a chart?
A
chart
can be defined as a
graphical
representation for
data
visualization, such that the data is represented with symbols as bars lines in line chart, or slices in a pie chart"
It is used to represent tabular numeric data and functions or other kinds of quality structure, providing different information.
The tools used in a chart includes;
Info-gram
tableau
Grafana
Chartist,
FusionCharts,
Datawrapper
ChartBlocks
Hence, a
chart
is a graphic representation of data.
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chart
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What is the remainder when x³ 3x² 4x 6 x 3?
The expression x³ 3x² 4x 6 can be expanded to x³ + 3x² - 4x - 6. When this expression is evaluated for x = 3, the result is 24, so the remainder is 0.
The expression x³ 3x² 4x 6 can be expanded to x³ + 3x² - 4x - 6. To find the remainder when this expression is evaluated, we must first substitute in a value for x. For this example, let x = 3. When we substitute 3 for x, the expression becomes 3³ + 3x² - 4(3) - 6. We can simplify this expression by performing the operations in order of operations. First, we can calculate 3³, which is equal to 27. Next, we can calculate 3x², which is equal to 27. Subtracting 4(3) from 27 gives us 15. Finally, subtracting 6 from 15 gives us 9.
The remainder of evaluating
x³ 3x² 4x 6 for x = 3 is 9.
x³ 3x² 4x 6 = 3³ + 3x² - 4(3) - 6 = 27 + 27 - 12 - 6 = 24
Remainder = 24 - 3 = 0
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What is the formula for finding the area of an isosceles triangle?
Answer:
base x height also A=1/2bh
Step-by-step explanation:
that’s the formula
Please help I will give brainliest
Answer:
cos(x) = r/t
sin(x) = s/t
tan(x) = s/r
Step-by-step explanation:
Background info:
This question becomes simple when we remember SohCahToa.
Soh stands for Sine = Opposite/ Hypotenuse
Cah stands for Cosine = Adjacent/ Hypotenuse
Toa stands for Tangent = Opposite/ Adjacent
Solving:
1. Cosine of angle x (think Cah)
The adjacent side is r and the hypotenuse is t.
so the answer is r/t
2. sine of angle x (think Soh)
The opposite side is s and the hypotenuse is t.
so the answer is s/t
3. Tangent of angle x (think toa)
The opposite side is s and the adjacent side is r.
so so the answer is s/r
The sum of 3 33 consecutive odd numbers is 69 6969. What is the third number in this sequence?.
The third number in this sequence is 23.
The sum of three consecutive odd numbers can be written as (2n-1) + (2n+1) + (2n+3) = 69, where n is a positive integer. Expanding the left side gives us 6n+1 = 69, which means n = 11. The third number in the sequence is (2n+1) = (2 × 11+1) = 23. Therefore, the third number in the sequence is 23.
In the given sequence, 1, –3, 9, –27, 81,..., each number is multiplied by -3 to get the next one in the sequence. Since the absolute values of the numbers in the sequence are increasing, the sequence is diverging to an infinite value, either positive or negative. Therefore, it can be concluded that the given sequence is a divergent sequence.
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What are the factors of 6x² 5x 6?
Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .Quadratics can be defined using an equation of a second-degree polynomial.
what is quadratic equation ?The mathematical action known as "squaring," which is typically used to describe a quadratic problem, involves multiplying a variable by itself. This lexicon is based on the idea that the area of a square is equal to the product of the lengths of its sides. The Latin term quadratum, which means square, is where the word "quadratic" comes from.
here
= 6x² - 5x- 6
= 6x² - 9x + 4x - 6
= 2 ( 2x - 3 ) + 3x ( 2x - 3 )
= (3x+2) ( 2x - 3 )
So , Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .
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Determine the domain of the following graph:
Step-by-step explanation:
the domain of a function is the interval or set of all valid x (input) values.
the range of a function is the interval or set of all valid y (function result) values.
the graph shows us that the x values are continuously between -5 and +3.
and the end points are filled, so, they are to be included as valid points (via the <= or >= signs).
so, the domain is
-5 <= x <= 3
help me with this please
The evaluated value of the expression b² - 4ac when a = -2, b = -4 and c = 1 is 24.
How to evaluate expression?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
Therefore, let's evaluate b² - 4ac when a = -2, b = -4 and c = 1.
Hence,
b² - 4ac = (-4)² - 4(-2)(1) = 16 + 8 = 24
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A student uses a solution that contains 16 grams of water to conduct an evaporation experiment. At the end of one hour the amount of water in the solution has decreased by 3.5%
Answer:
Step-by-step explanation:
.035*16=.56 solution has decreased for this part
16 divided by 3.5⁶66677⁷54776367
Step-by-step explanation:
4_35665567
please help me with this problem
Answer:
40 orange marbles
Step-by-step explanation:
We know for every 12 marbles, we have 5 orange marbles and 7 green marbles
Now we have 56 green marbles. To get from 7 to 56, we take 7 times 8.
So, we do the same take 5 times 8 = 40 orange marbles
So, it contains 40 orange marbles!
Emma had to finish her 249-page novel by Friday. She had already read 166 pages. Write and solve an equation to show how many pages Emma had left to read by Friday.
p + 166 = 249; p = 83 pages
p − 166 = 249; p = 415 pages
p over 166 equals 2; p = 332 pages
83p = 166; p = 2 pages
Answer:
p + 166 = 249
p = 83 pages
Step-by-step explanation:
We know that she has to finish 249 pages novel and read 166.
So, let p represent the number of pages left to read; we have the equation
p + 166 = 249
Now let's solve by subtracting 166 from both sides
p = 83 pages
So, Emma had 83 pages left to read by friday
Are there 2 answers to a quadratic equation?
The above quadratic equation has two solutions, as shown by the question Yes.
A quadratic equation is what?A second-order polynomial equation with a single variable, x, is known as a quadratic equation.
ax2 + bx + c = 0 is a quadratic equation in standard form.
x stands for an unknown (an variable)
With respect to known numbers, a, b, and c, where a 0
The polynomial's number of solutions is influenced by the equation's highest possible power given in the question.
The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation.
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