We conclude that the graph of f(x) is the graph of g(x) translated 3 units upwards.
How do relate the graphs of f(x) and g(x)?Here we have the functions:
[tex]f(x) = log(x) + 3\\\\g(x) = log(x)[/tex]
And we want to find a relation between them.
Remember that a vertical translation of N units (the sign of N defines the direction of the translation) is written as:
[tex]f(x) = g(x) + N[/tex]
In this case, we can see that N = 3, it is positive, so the translation is upwards. (This means that the whole graph of the function f(x) is translated upwards 3 units in the coordinate axis)
Then we conclude that the relation between the graphs of the given functions is that the graph of f(x) is the graph of g(x) translated 3 units upwards.
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Tell whether the given value is a solution to the inequality.
y + 5 > 8l; y = 1
The solution of the inequality equation is determined as y > 3.
What is the solution of the inequality equation?A solution for an inequality in y is a number such that when we substitute that number for y we have a true statement.
For the given inequality equation, which is;
y + 5 > 8
The solution of the inequality equation is calculated as follows;
y + 5 > 8
Subtract 5 from both sides of the equation as shown below;
y + 5 - 5 > 8 - 5
y > 3
The solution of the inequality equation is determined as 3, so we can conclude that any value less than 3 is not true and the proposed solution of 1 is not true or correct for the inequality equation.
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A popular brand has introduced a new design of jeans. All major stores have stocked the jeans because the brand usually sells very well. But the cost of these jeans is much higher than those of other brands, so people don't buy them.
The price of the jeans will decrease because supply is greater than demand hence the stores will sell them at discounted prices.
How do we calculate?The store owners would be forced to cut pricing if the jeans weren't purchased at all or as frequently as the other brands. Either they choose that choice, return the goods if possible or just toss the jeans away. It generally takes some trial and error to determine the proper price.
For instance, the owner may lower the price to $75 and test whether the 25% discount works or not if the jeans initially sell for $100 and nobody buys them for a week.
The price might remain there if people continue to buy and if not, the cost might decrease even further.
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A
4
B
10
2
AABC - ATUV
Find x.
T
C
6
U
X = [?]
X
The unknown length of the similar figure is:
x = 15 units
How to find the unknown length of the similar figure?Two figures are similar if they have the same shape but different sizes. The corresponding angles are equal and the ratios of their corresponding sides are also equal.
Using the above concept, we can equate the ratio of the corresponding sides and solve for the unknown lengths. That is:
TV/AC = TU/AB
x/10 = 6/4
x/10 = 1.5
x = 10 * 1.5
x = 15 units
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need help my dad owns this app
The volume of the solid is given as follows:
55 ft³.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The total volume would be given as follows:
V = 9 x 6 x 1.25
V = 67.5 ft³.
The volume of the removed part is given as follows:
V = 1.25 x 2.5 x (9 - 3 - 2)
V = 12.5 ft³.
Hence the volume of the solid is given as follows:
67.5 - 12.5 = 55 ft³.
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how much money deposited now will provide payment of Rs. 15000 at the end of each half year for 10 years, if interest is 16% compounded six-monthly
The amount of money that will produce Rs. 15000 at the end of 6 month for 10years at 16% is Rs. 3750
What is Compound interest?Compound interest is the interest you earn on interest.
For example, if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.
Compound interest is expressed as;
A = P( 1+r/n) ^{nt}
where A is the amount
n is the number of time its compounded
t is time
A = 15000
r = 16/100 = 0.16
n = 6/12 = 0.5
t = 10 years
15000 = P( 1 + 0.16/0.5) ^{ 0.5× 10}
15000 = P( 1 + 0.32)⁵
15000 = P( 1.32)⁵
15000 = 4P
P = 15000/4
P = Rs. 3750
Therefore the amount that will be deposited to give Rs. 15000 is Rs. 3750.
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Find the sum below. Explain how you got this answer
-11 + 3 + 10 + (-25) + 48 =
Answer:
25
Step-by-step explanation:
There are only additions, so do each addition, in the order it appears, from left to right.
-11 + 3 + 10 + (-25) + 48 =
= -8 + 10 + (-25) + 48
= 2 + (-25) + 48
= -23 + 48
= 25
During the winter, if the low temperature outside is a °C, the daily cost to heat a
building can be determined using the function f(x) = 5 (1.3) * . Find and
interpret the given function values and determine an appropriate domain for the function.
round all function values to the nearest hundredth.
f:7)= __, meaning when the low temp outside is __ celsius it would cost $__ to heat the building. this interpretation _______________ in the context of your problem.
f(9.5)=___, meaning when the low temp outside is ___ celsius it would cost & __ to heat the building. this interpretation _______________ in the context of the problem.
based on the observations above it is clear that an appropriate domain for the function is —————
PLEASE HELP
The values of the function are 5 and 1.5 and the domain is,
⇒ - ∞ < x < ∞
Here, The equation of the function is given as
f(x) = 5 (1.3)ˣ
The above function is an exponential function.
An exponential function is represented as
f(x) = abˣ
Where
a represents the initial value, b represents the rate of growth or decay
While x and f(x) are the input and output values
Hence, By comparison, we have
a = 5 and b = 1.3
This means that the function values are 5 and 1.3.
Since, the function is an exponential function.
The domain of an exponential function is the set of all real values
Hence, the domain of f(x) is the set of all real values.
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Which transformation maps △UVW to △EFG?
A. (x, y) ⟶ (0.5x, 0.5y)
B. (x, y) ⟶ (–0.5x, 0.5y)
C. (x, y) ⟶ (2x, 2y)
D. (x, y) ⟶ (–2x, 2y)
Based on the analysis, the correct transformation that maps triangle △UVW to triangle △EFG is option C: (x, y) ⟶ (2x, 2y), which represents an enlargement or dilation of the figure.
To determine which transformation maps triangle △UVW to triangle △EFG, we need to analyze the given options and understand the effects of each transformation.
A. (x, y) ⟶ (0.5x, 0.5y):
This transformation scales the coordinates of a point by a factor of 0.5 in both the x and y directions.
It represents a reduction or contraction of the figure.
Triangle △UVW would be scaled down to a smaller size, so option A is not the correct transformation.
B. (x, y) ⟶ (–0.5x, 0.5y):
This transformation reflects the coordinates of a point across the y-axis and scales the x-coordinate by a factor of -0.5 and the y-coordinate by a factor of 0.5.
It represents a reflection and scaling.
Triangle △UVW would be reflected across the y-axis and scaled, which does not match the transformation to △EFG.
Therefore, option B is not the correct transformation.
C. (x, y) ⟶ (2x, 2y): This transformation scales the coordinates of a point by a factor of 2 in both the x and y directions.
It represents an enlargement or dilation of the figure.
Triangle △UVW would be scaled up to a larger size, which aligns with the transformation to △EFG.
Therefore, option C could be the correct transformation.
D. (x, y) ⟶ (–2x, 2y):
This transformation reflects the coordinates of a point across the x-axis and scales the x-coordinate by a factor of -2 and the y-coordinate by a factor of 2.
It represents a reflection and scaling.
Triangle △UVW would be reflected across the x-axis and scaled, which does not match the transformation to △EFG.
Thus, option D is not the correct transformation.
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The weight (in kilograms) of 14 patients were measured as 59, 63, 61, 62, 58, 60, 58, 57, 57, 56, 50, 69, 58 and 50. What is the range weight (in kilograms) of these patients?
Answer:
57 kilograms. .........................................................................kg
17 in. 16 in. 14 in.
The surface area of the rectangular prism is 1468 square inches
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
17 in by 16 in by 14 in
The surface area of the rectangular prism is calculated as
Area = 2 * (17 * 16 + 17 * 14 + 16 * 14)
Evaluate
Area = 1468
Hence, the area is 1468 square inches
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Question
What is the surface area of this rectangular prism?
17 in. by 16 in. by 14 in.
................................................
Answer:
4,12,36,108,324.....
Step-by-step explanation:
The sequence represented by the equation [tex]a=4(3)^{n-1}[/tex]is a geometric sequence with first term 5 and common ratio 3. The first 4 terms of the sequence are:
[tex]a_1 = 4(3)^{1-1} =4(3)^0 = 4[/tex]
[tex]a_2 =4(3)^{2-1} = 4(3)^1 = 12[/tex]
[tex]a_3 =4(3)^{3-1} = 4(3)^2 = 36[/tex]
[tex]a_4 = 4(3)^{4-1} =4(3)^3 = 108[/tex]
[tex]a_5=4(3)^{5-1} =4(3)^4=324[/tex]
The sequence can be written as:
[tex]a_n = 4(3)^{n-1}[/tex]
where n is the term number.
Therefore, the sequence is 4,12,36,108,324.....
Answer:
The answer is 4,12,36,108,324
Step-by-step Explanation:
a1=4(3)¹‐¹=4(3)⁰=4
a2=4(3)²‐¹=4×3=12
a3=4(3)³‐¹=4(3)²=4×9=36
a4=4(3)⁴‐¹=4(3)³=4×27=108
a5=4(3)⁵‐¹=4(3)⁴=4×81=324
i need some help here
The value of x, considering the Pythagorean Theorem, is given as follows:
x = 9.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The sides for the problem are given as follows:
15 and 8 (segment of 8 is the radius, which is the distance from the center to a point on the circumference of the circle).
Hence the hypotenuse is obtained as follows:
h² = 15² + 8²
h² = 289
h = 17.
Hence the value of x is obtained as follows:
x = 17 - 8
x = 9.
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Please help me with this I am on the verge of giving up because of it. Simplify and rationalize the denominnator, the answer should not have negative exponents
The exponential value equation is A = 1/√x = 1/x^(-1/2)
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
A = x ^ ( 1/6 ) / x ^ ( 2/3 )
On simplifying , we get
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
So , A = x ^ ( 1/6 - 2/3 )
On further simplification , we get
A = x ^ ( -3/6 )
A = x ^ ( -1/2 )
So , the value of A is
A = 1/√x
Hence , the exponential equation is solved
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The length and breadth of a rectangular flower bed are 16m and 9 m, respectively. How many plants can be planted in it, if each plant requires a space of 1.2m x 1m?
The calculated number of plants the flower bed can contain is 120
Calculating hw many plants can be planted in itFrom the question, we have the following parameters that can be used in our computation:
Dimensions = 16 m by 9 m
So, the area of the flower bed is
Area = 16 * 9
Evaluate
Area = 144
Also, we have
Each plant requires a space of 1.2m x 1m?
This means that
Plant area = 1.2 * 1
Plant area = 1.2
So, we have
Plants = 144/1.2
Evaluate
Plants = 120
Hence, the number of plants is 120
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Answer:
Step-by-step explanation:
To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.
The area of the flower bed is calculated by multiplying its length and breadth.
So, the area of the flower bed is 16m x 9m = 144 sq.m.
Each plant requires a space of 1.2m x 1m = 1.2 sq.m.
Therefore, the number of plants that can be planted in the flower bed is:
144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.
So, you can plant 120 plants in the rectangular flower bed.
Anybody know this? Find the first four terms of the sequence t/n=n(6n-2) the n is below the t btw
The first four terms of the sequence t/n = n(6n - 2) are: 4, 20, 48, 88.
How to find st four terms of the sequenceLet's substitute n = 1:
t/1 = 1(6(1) - 2)
t = 1(6 - 2)
t = 4
The first term of the sequence (when n = 1) is 4.
Now, let's substitute n = 2:
t/2 = 2(6(2) - 2)
t = 2(12 - 2)
t = 2(10)
t = 20
The second term of the sequence (when n = 2) is 20.
Next, let's substitute n = 3:
t/3 = 3(6(3) - 2)
t = 3(18 - 2)
t = 3(16)
t = 48
The third term of the sequence (when n = 3) is 48.
Lastly, let's substitute n = 4:
t/4 = 4(6(4) - 2)
t = 4(24 - 2)
t = 4(22)
t = 88
The fourth term of the sequence (when n = 4) is 88.
Therefore, the first four terms of the sequence t/n = n(6n - 2) are: 4, 20, 48, 88.
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What is the value of x?
Answer:
x = 24.5
Step-by-step explanation:
27/(x + 7) = (27 - 6)/x
27x = (x + 7)(21)
27x = 21x + 147
6x = 147
x = 24.5
Answer:
x = 31.5
Step-by-step explanation:
given a line parallel to a side of a triangle and it intersects the other two sides then it divides those sides proportionally , that is
[tex]\frac{6}{27-6}[/tex] = [tex]\frac{7}{x}[/tex]
[tex]\frac{6}{21}[/tex] = [tex]\frac{7}{x}[/tex] ( cross- multiply )
6x = 21 × 7 = 147 ( divide both sides by 6 )
x = 24.5
100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
For this problem, you need an on-hand calculator.
Problem:
sin (pi/8)
Step 1: divide pi by 8.
[tex]\pi[/tex]/8
=0.39269908169
Step 2: Find Cosine of (0.39269908169)
This is the part where you need a calculator.
Locate the SIN button on your graphing calculator.
Press the SIN button, then continue to type 0.39269908169 after the parenthesis.
The calculator gives a value of .0068538383
Final answer:
0.068538383
Pls Need this ASAP
When purchasing a home, you need a loan for $80,000. The interest rate of the
loan is 8% and you are required to make monthly payment of $587.
Answer:
1) 5m
2) 0.25tan
Step-by-step explanation:
HELP ASAP PLEASE
LATE ASSIGNMENT
The measure of angle ABC is given as follows:
m < ABC = 55º.
How to obtain the measure of angle ABC?First we look to the exterior angle of angle C in the bottom parallel line, as a ray is formed, hence the missing angle measure is given as follows:
50 + 75 + x = 180
125 + x = 180
x = 55º.
The exterior angle relative to angle B is supplementary with the angle of 55º, as they are consecutive angles, hence it’s measure is obtained as follows:
y + 55º = 180
y = 125º.
By the exterior angle theorem, an interior angle is supplementary with it’s respective exterior angle, hence the measure of angle ABC is given as follows:
m < ABC + 125 = 180
m < ABC = 55º.
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A bulb manufacturer claims that the lives of its bulbs are normally distributed with a mean of 8000 hours and a standard deviation of 400 hours. A random sample of 16 bulbs had an average life of 7920 hours. If the manufacturer’s claim is correct,
a. What is the sampling distribution of the sample mean? Sketch the normal distribution. Show the mean and s.d. in the figure.
b. what is the probability of finding a sample mean of 7920 or less? Show the probability in the figure mentioned above.
e
B
0
14. The table shows the number of inches of
rain over five months. What would be an
appropriate display of the data? Explain.
(Lesson 2)
Month
Number
of Inches
of Rain
Jan. Feb. Mar.
1.5
2.2
3.6
Apr.
5.3
May
4.8
The graph of the given function is attached.
Given is a function for the rainfall in 5 months in inches.
We need to display the data,
So, as we can see that the data is not showing any proportion or pattern,
So, it can be displayed as a line chart.
Hence the chart is attached for the function.
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A telephone pole is 54 feet tall. A guy wire runs 83 feet, from point A at the top of the telephone pole, to the ground at point B. The base of the telephone pole is at point C. Triangle ABC is a right triangle.
How far from the base of the telephone pole, to the nearest tenth of a foot, is the guy wire secured to the ground at point B?
Okay, let's break this down step-by-step:
* The telephone pole is 54 feet tall
* The guy wire runs 83 feet from point A (top of pole) to point B (ground)
* So the hypotenuse (AB) of the right triangle is 83 feet
* The opposite side (AC) is 54 feet (height of pole)
To find the adjacent side (BC), we use the Pythagorean theorem:
a^2 + b^2 = c^2
54^2 + BC^2 = 83^2
Solving for BC gives:
BC = sqrt(83^2 - 54^2) = sqrt(1296 - 2916) = sqrt(1620) = 40 feet
So the guy wire is secured 40 feet from the base of the telephone pole.
Rounded to the nearest tenth is 40.0 feet.
Therefore, the final answer is:
40.0
Let me know if you have any other questions!
Find area of the shape
Answer:
130.4
Step-by-step explanation:
6 x 14 = 84
8 x 4 = 32
(4 x 7.2)/2 = 14.4
What are the solutions of the equation 2 log x = log (5x-6)? Select all that apply.
A x=1
B. x=2
C. x= 3
D. x = 5
E. x=6
Answer:
B, C
Step-by-step explanation:
x^2 = 5x - 6
x = 2 or x = 3
What is the value of x?
Solving a simple equation, we can see that x = 35.
How to find the value of x?The 3 lines with an arrow that go to the left are parallel lines, thus, the relation between the sets of values in each of the sides must be the same ones.
Then we can take the quotients between the respective values, and these quotients must be equal, so we can write:
30/12 = x/14
And now we can solve that equation for x, we will get:
x = 14*(30/12)
x = 35
That is the value of x.
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Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee
Darlene's net proceeds from the investment into shares would be $ 8, 279 .
How to find the net proceeds ?First, find the initial broker fee:
= Initial investment × Broker fee rate
= 20, 000 x 1. 5 %
= 20, 000 x 0. 15
= $ 300
The total fees incurred to buy and sell are:
= 300 initial broker + 21 later broker
= $ 321
The net proceeds would then be:
= Final value of stock - Initial investment - Total fees
= 28, 600 - 20, 000 - 321
= 8, 600 - 321
= $ 8, 279
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Full question is:
Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee. She sells her stock when it increases to $ 28,600 two years later, and uses a discount broker who charges $21 per trade. Compute Darlene's net proceeds after the broker fees are taken out.
Find the Value of x. Round to the nearest tenth.
hyp = x
28°
11
The calculated value of x in the right triangle is 12.5
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The value of x can be calculated using the following cosine rule
So, we have
cos(28) = 11/x
make x the subject of the formula
So, we have
x = 11/cos(28)
Evaluate the quotient
This gives
x = 12.5
Hence, the value of x is 12.5
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lim[tex]\frac{n^{2} +4n-5}{3n^{3}+n^{2}+7 }[/tex]
Step-by-step explanation:
limit for n going to what ?
I think you mean n going to ±infinity.
for very large n (when n goes to infinity) such a fraction is reduced to the ratio of the terms with the highest exponents of n. the terms with lower exponents simply get less and less impact with growing n, and fade away for really, really large n going to infinity.
so, this limit evaluation is reduced to
lim n²/(3n³ + n²) = 1/(3n + 1)
which is again for very large n
lim 1/(3n), which goes to 1/infinity = 0
the same for going to 1/-infinity = 0
if you meant e.g. limit for n going to 0, then for the limit we set n to 0 and see, that all terms are turning 0, except for the constants -5 in the numerator and +7 in the denominator.
so, that limit is then
-5/7 = -0.714285714...
A right triangle has side lengths 45 millimeters, 108 millimeters, and 117 millimeters. What is the length of the hypotenuse and why?
117 millimeters, because it is listed last.
117 millimeters, because the hypotenuse is the longest side.
45 millimeters, because 45 is half of 90 and a right angle is 90°.
45 millimeters, because the hypotenuse is the shortest side.
Submit
The length of the hypotenuse of the given right triangle is 117 millimeters because it is the longest side and it satisfies the conditions of the Pythagorean theorem.
The length of the hypotenuse of a right triangle with side lengths 45 millimeters, 108 millimeters, and 117 millimeters is 117 millimeters.
The hypotenuse of a right triangle is always the side opposite the right angle, and it is the longest side in a right triangle.
In this case, the side lengths are given as 45 millimeters, 108 millimeters, and 117 millimeters.
By comparing the lengths, we can see that 117 millimeters is the longest side, which makes it the hypotenuse.
To further understand why the hypotenuse is the longest side, we can refer to the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Mathematically, it can be written as c² = a² + b²,
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In this case, if we square the lengths of the sides, we get 45² = 2025, 108² = 11664, and 117² = 13689.
By comparing these values, we can see that 13689 is the largest, which corresponds to the length of the hypotenuse, 117 millimeters.
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A jar contains 8 pennies, 3 nickels, 5 dimes, and 2 quarters. If one coin is chosen from the jar, how many ways are there to get more than 4 cents
Answer: The jar contains a total of 18 coins (8 pennies + 3 nickels + 5 dimes + 2 quarters). To get more than 4 cents, we need to choose a nickel, dime, or quarter. There are 3 nickels, 5 dimes, and 2 quarters, for a total of 10 coins that satisfy this condition. Therefore, there are 10 ways to choose a coin from the jar that is more than 4 cents.