The matching of each transformed function is as follows;
g(x) = 2f(x) → y-intercept at (0,2)
h(x) = f(x) + 2 → asymptote of y=2
j(x) = f(x + 2) → y-intercept at (0,4)
m(x) = function decreases as x increases
How to match transformations?A function is simply defined as a relationship between the inputs and the outputs. Now, we want to map each transformed function.
From the graph of this question as shown in the attached brainly link, the correct matching of each transformation of function f(x) = In x with a feature of the transformed function are as follows;
g(x) = 2f(x) → y-intercept at (0,2)
h(x) = f(x) + 2 → asymptote of y=2
j(x) = f(x + 2) → y-intercept at (0,4)
m(x) = function decreases as x increases
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I really had some trouble with this problem:( & I need some help
Lines RS, TV, and SW are shown.
10-
8-
R
S
6
4-
2-
-10-8-6-4-22-
2 4 6 8 10 x
T
-6
8
W
-10-
☎ do
N
Which statements are true about these lines? Select
three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
Answer:
b
Step-by-step explanation:
The statements true about the slopes and lines are
a) Line TV has a slope of 0.
b) Lines RS and TV are parallel.
c) Line SW has an undefined slope.
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be S ( 2 , 6 )
Let the second point be R ( -8 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - 6 ) / ( -8 - 2 ) = 0
So , the slope of line RS = 0
Let the point T = T ( -6 , -4 )
Let the point V = V ( 8 , -4 )
Slope m = ( -4 - (-4) ) / ( 8 - (-6) ) = 0
So , the slope of line TV = 0
And , the lines RS and TV are parallel as they have the same slope
Now , the x coordinate of the point S and W does not change
So , it has an undefined slope
Hence , the equation of line is solved
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The complete question is attached below :
Lines RS, TV, and SW are shown.
Which statements are true about these lines? Select
three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
An ordinary die is a cube with numbers 1 through 6 on the sides. Imagine that the die is rolled twice in sucession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
What is the probability that the sum is not divisible by 2 and not divisible by 4?
Answer:
1/2Step-by-step explanation:
NOTE : we have 6×6=36 possible outcome.
we can resume the set of outcomes in the table below :
Then
the probability that the sum is not divisible
by 2 and not divisible by 4 :
= 18/36
= 1/2
5. Solve for x.
21
4
Answer: 10
Step-by-step explanation:
By the geometric mean theorem, if we let the length of the altitude to the hypotenuse be [tex]y[/tex], this means that [tex]y^{2}=84 \longrightarrow y=\sqrt{84}[/tex].
So, by the Pythagorean theorem, [tex]x=\sqrt{(\sqrt{84})^{2}+4^{2}}=\boxed{10}[/tex]
A sinusoidal function whose period is 4π, maximum value is 6, and minimum value is -2 has a y intercept of 6. What is the equation of the function described?
Equation of the function: f(x) = 4 sin (x/2) + 6.
What is sinusoidal function ?The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. It is named based on the function y=sin(x).
Given: max value= 6, min value= -2, y-intercept= 6.
As, standard form f(x) = A sin (ωx +φ) + k,
where A is the amplitude, ω is the angular velocity with ω=2πf.
Now,
A = |6- (-2)/2|
A = |6 +2/2| = 8/2
A = 4
Also, ω:
The period of a sinusoidal is T = 1/f
so, f = 1 / T
ω = 2πf
ω = 2π ( 1/T) with T = 4π
ω = 2π (1/(4π) = 2π (2)
ω = 1/2
The y-intercept k = 6
So, equation with values A =4, ω = 1/2, k = 6, φ = 0.
f(x) = A f(x)
f(x) = A sin (ωx +φ) + k
f(x) = 4 sin (x/2) + 6.
Hence, equation of the function f(x) = 4 sin (x/2) + 6.
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Suppose there is a simple index of three stocks, stock ABC, stock XYZ, and stock QRS. Stock ABC opens on day 1 with 8000 shares at $4.25 per share. Stock XYZ opens on day 1 with 5000 shares at $2.90 per share. Stock QRS opens on day 1 with 2000 shares at $6.40 per share. The price of stock ABC on day 8 begins at $3.90. The price of stock XYZ on day 8 begins at $2.50. Stock QRS opens on day 8 with a price of $6.10 per share. Assume that each stock has the same number of shares that it opened with on day 1. What is the rate of change of this simple index over 1 week?
The rate of change of this simple index over 1 week is - 8.81%
What is the rate of change ?The rate of change is the ratio of the difference in the value of the simple index to the original value of simple index.
Total value of the simple index at day 1 = (8000 x $4.25) + (5000 x $2.90) + (2000 x $6.40) = $61,300
Total value of the simple index at day 8 = (8000 x $3.90) + (5000 x $2.50)+(2000*6.10) = 55900
the rate of change of this simple index over 1 week
= (55900-61300)/ 61300 * 100 %
= -8.81 %
the rate of change of this simple index over 1 week is - 8.81%
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what is the area of the figure?
Answer:
area = 62ft
Step-by-step explanation
so you section the polygon into a big rectangle and 2 small rectangles
the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft
the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft
now add the areas you got, 50+12 which is 62ft
hope this helps:)
9. Find the area:
25
19
13
Answer:
162.5
Step-by-step explanation:
25=height
13=base
to find the area of a triangle you do (h(b)b)/2
Zahid started the construction of an equilateral triangle inscribed in a circle. Which segments need to be drawn to create the triangle?
To finish his construction, Zahid needs to draw segments df ,
, and
.
The rule for construction of Inscribed equilateral triangle
Draw 6 marks as per the picture.Then join one with next alternative leaving second .Means if marks are from 1 to 6 then
133551Or
244662Now
Here the rest two segments are
DFBFBDAnswer:
FB and DB
Step-by-step explanation:
got it right on the test
Write each expression in radical form
[tex]\sqrt[4]{6^5}[/tex]
Step-by-step explanation:
This expression in radical form :4√65 =2.838412
If the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units, using integration find the value of a, where a > 0.
Answer:
a=2
Step-by-step explanation:
[tex]area=2\int\limits^a_b {y} \, dx =2\int\limits^a_b {\sqrt{4ax} } \, dx \\=2 \times 2\sqrt{a} \frac{x^{\frac{3}{2} } }{\frac{3}{2} } ~from~~b~to~a\\=\frac{8}{3}\sqrt{a} (a^{\frac{3}{2} } -b^{\frac{3}{2} } )\\=\frac{8}{3} \sqrt{a}( (4a)^{\frac{3}{2} } -0)\\=\frac{8}{3} \sqrt{a} ((4a)\sqrt{4a} -0)\\=\frac{32 a}{3} \times 2a\\=\frac{64}{3} a^2[/tex]
[tex]\frac{64}{3} a^2=\frac{256}{3} \\a^2=\frac{256}{3} \times \frac{3}{64} =4\\a=2 (a > 0)[/tex]
the curve is a right parabola.
here b=0,and a=4a for x
we are finding the area between x-axis and x from 0 t0 4a.
curve is symmetrical about x-axis so we multiply by 2.
If the area of the region bounded by the curve [tex]y^2 =4ax[/tex] and the line [tex]x= 4a[/tex] is [tex]\frac{256}{3}[/tex] Sq units, then the value of [tex]a[/tex] will be [tex]2[/tex] .
What is area of the region bounded by the curve ?An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.
Area bounded by the curve [tex]=\int\limits^a_b {x} \, dx[/tex]
We have,
[tex]y^2 =4ax[/tex]
⇒ [tex]y=\sqrt{4ax}[/tex]
[tex]x= 4a[/tex],
Area of the region [tex]=\frac{256}{3}[/tex] Sq units
Now comparing both given equation to get the intersection between points;
[tex]y^2=16a^2[/tex]
[tex]y=4a[/tex]
So,
Area bounded by the curve [tex]= \[ \int_{0}^{4a} y \,dx \][/tex]
[tex]\frac{256}{3} =\[ \int_{0}^{4a} \sqrt{4ax} \,dx \][/tex]
[tex]\frac{256}{3}= \[\sqrt{4a} \int_{0}^{4a} \sqrt{x} \,dx \][/tex]
[tex]\frac{256}{3}= \[2\sqrt{a} \int_{0}^{4a} x^{\frac{1}{2} } \,dx \][/tex]
[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{1}{2}+1 } }{\frac{1}{2}+1 }\end{array}\right] _{0}^{4a}[/tex]
[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{3}{2} } }{\frac{3}{2} }\end{array}\right] _{0}^{4a}[/tex]
[tex]\frac{256}{3}= 2\sqrt{a} *\frac{2}{3} \left[\begin{array}{ccc}(x)^{\frac{3}{2}\end{array}\right] _{0}^{4a}[/tex]
On applying the limits we get;
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} \left[\begin{array}{ccc}(4a)^{\frac{3}{2} \end{array}\right][/tex]
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} *\sqrt{(4a)^{3} }[/tex]
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} * 8 *a^{2} \sqrt{a}[/tex]
[tex]\frac{256}{3}= \frac{4}{3} * 8 *a^{3}[/tex]
⇒ [tex]a^{3} =8[/tex]
[tex]a=2[/tex]
Hence, we can say that if the area of the region bounded by the curve [tex]y^2 =4ax[/tex] and the line [tex]x= 4a[/tex] is [tex]\frac{256}{3}[/tex] Sq units, then the value of [tex]a[/tex] will be [tex]2[/tex] .
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T=mv^2/L
Write an equation that shows the given formula solved for V
Answer:
v = √(LT/m)
Step-by-step explanation:
Given :
T = mv²/LMultiply both sides with L :
T × L = mv²/L x LLT = mv²Divide both sides by m :
LT × 1/m = mv² × 1/mLT/m = v²Take the square root on each side :
√v² = √(LT/m)v = √(LT/m)Answer:
[tex]v = \sqrt{ \frac{tl}{m} } [/tex]
Step-by-step explanation:
[tex]t = \frac{mv {}^{2} }{l} \\ making \: v \: the \: subject \\ t \times l = mv {}^{2} \\ dividing \: bothsides \: by \: m \\ \frac{tl}{m} = \frac{mv {}^{2} }{m} \\ v {}^{2} = \frac{tl}{m} \\ finally \\ v = \sqrt{ \frac{tl}{m} } [/tex]
I need a thorough explanation for question 4 please. It’s about Operations of Powers/Exponents.
Simplify
I need help for finals
Answer:
goto gauth maths and ask again
Two exponential functions are shown in the table.
X
f(x)=2*
g(x) =
2
2
4
1
2
0
-1
-2
2
71111
4
141212
4
Which conclusion about f(x) and g(x) can be drawn
from the table?
O The functions f(x) and g(x) are reflections over the x-
axis.
O The functions f(x) and g(x) are reflections over the y-
axis.
O The function f(x) is a decreasing function, and g(x) is
an increasing function.
O The function f(x) has a greater initial value than g(x).
Based on the table, a conclusion which can be drawn about f(x) and g(x) is that: B. the functions f(x) and g(x) are reflections over the y-axis.
How to compare the functions f(x) and g(x)?In Mathematics, two functions are considered to be reflections over the y-axis under the following condition:
If, f(-x) = g(x).
Evaluating the given functions, we have:
f(x) = 2ˣ
f(-x) = 2⁻ˣ = ½ˣ = g(x).
Similarly, two functions are considered to be reflections over the x-axis under the following condition:
If, -f(x) = g(x).
Evaluating the given functions, we have:
f(x) = 2ˣ
-f(x) = -2ˣ ≠ g(x).
Therefore, we can logically conclude that the two functions f(x) and g(x) are considered to be reflections over the y-axis but not the x-axis.
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A. 36
B. 52
C. 148
D. 168
Answer:
B) 52
Bodmas rule:
BracketsOrderDivisionMultiplicationAdditionSubtractionSolving Steps:
⇒ 2 × (3 - 1)⁴ + 5 × 4
⇒ 2 × (2)⁴ + 5 × 4
⇒ 2 × 16 + 5 × 4
⇒ 32 + 20
⇒ 52
Option B
help me with this please
Answer:
A- 17/24 sugar all together
B- yes the bowl would be big enough because when you add all the ingredients together it equals 3 5/24 and it's less than 3 1/2.
Select whether the pair of lines is parallel, perpendicular, or neither. x=−2, y=10
Answer:
perpendicular
Step-by-step explanation:
x = -2 is a vertical line at x = -2
y is a horizontal line the two lines are perpindicular
the lines x=−2, y=10 are perpendicular to each other.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Here, The given equations are :
x=−2 and y=10
First, consider x = -2 equation :
equation x = -2 is a vertical line, parallel to x = 0 line and perpendicular to line y = 0.
Consider second line y = 10 :
line y = 10 is horizontal line and is parallel to line y = 0 and is perpendicular to line x = 0.
Therefore, the lines x=−2, y=10 are perpendicular to each other.
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70 POINTS !!! Measure each angle and write the measure on the line.
Answer:
See below
Step-by-step explanation:
You will just need to use your protractor to measure the given angles..
Here is some gross guesses starting with top row
45 120 100 25 90 80 135 120 °
What causes the economy to move from its short-run equilibrium to its long-run equilibrium?
Answer:
Nominal wages, prices, and perceptions adjust upward to this new price level
Step-by-step explanation:
In the given triangles, PR ≅ AC and ∠P ≅ ∠A.
Which additional fact is needed in order to use the ASA criterion to prove that the two triangles are congruent?
Answer:
option c and d are correct
Step-by-step explanation:
if there is only one choosing option you can choose option c
Which function has the same domain as y= 2√x?
Oy= √2x
O y=2³√x
0₁y = √x-2
O y=³√x-2
The option first is correct because y= 2√x and y= √2x have same domain which is x ≥ 0.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
y= 2√x
From the above function the domain should be:
x ≥ 0 (because square root of negative values does not exist)
The function:
y = √(2x)
2x ≥ 0
x ≥ 0
Thus, the option first is correct because y= 2√x and y= √2x have same domain which is x ≥ 0.
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can someone help me on part B please? I've done the answer to the rest please thanks!
Answer:
84 circular tiles are needed to make pattern number 20
4(20+1)
Step-by-step explanation:The number of circular tiles is 1 more than the pattern number on each side of the square.
circular tiles = 4(n +1)
2/3(cx+1/2)-1/4=5/2 solve
Answer:
2/3(cx+1/2)-1/4=5/2. CX=29/8
Help help help help help help help help
Multiply
k+3/4K - 2 (12k2 +2k -4)
Answer:
-204kk+3+32k/4k
Hope this helps!!
The Other Number Your first number was 8. Is the other one 0? How did we know that? Can we read your mind?
Answer:
???
Step-by-step explanation:
Which equation could generate the curve in the graph below?
y=3x² - 2x + 1
y=3x² - 6x +3
y=3x² - 7x + 1
y=3x² - 4x-2
What division problem does this area model represent?
Answer:
2,160 ÷ 36 = 60
Step-by-step explanation:
The division problem that this area model represents is,
2,160 ÷ 36 = 60
6. Janet spent $25, $30, $10, and $8 for
recreation in the last four weeks. What
was her average weekly expense for
recreation?
A. $12.50
B. $18.25
C. $25.25
D. $36.50
Answer:
B
Step-by-step explanation:
Total money spent = 25 + 30 + 10 + 8 = 73
Per week = 73 / 4 = 18.25
A bottle of coke cost 3/4 as much as a $5 milkshake. How much would 3 bottles of coke and 2 milkshakes cost?
Answer:
Total, 2 milkshakes, and 3 cokes would cost $12.50
Step-by-step explanation:
The cokes cost $11.50 and the milkshakes $10.00