1. Given the functions f(x) = log₂(5x) and g(x) = 5ˣ - 2 only statement c is true
2. The solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds
1. How to find which statements are true.Statement a
Since f(x) = log₂(5x) which is a logarithm function is undefined for (-∞, 0) and defined for (0, +∞) and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).
Also, since f(x) is decreasing on the interval (0, 1/5) while g(x) decreases on the interval (-∞, 0). So, they have do not have a common interval on (0, 1).
So, statement a. Both f(x) and g(x) decrease on the interval of (–∞, 1).
is false
Statement b
Since f(x) = log₂(5x) which is a logarithm function is defined for (0, +∞) and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).
So, the statement b Both f(x) and g(x) have the same domain of (0, ∞) is false
Statement c
Since f(x) = log₂(5x) which is a logarithm function has a range of (0, +∞). and g(x) = 5ˣ - 2 which is an exponential function is has a range of (-2, +∞).
So, they have a common interval of (0, +∞).
So, the statement c. Both f(x) and g(x) have a common range on the interval (–2, ∞) is true
Statement d
To find the x-intercept of f(x), we equate f(x) to zero.
So, f(x) = log₂(5x)
0 = log₂(5x)
2⁰ = 5x
1 = 5x
x = 1/5
To find the x-intercept of g(x), we equate g(x) to zero.
g(x) = 5ˣ - 2
0 = 5ˣ - 2
2 = 5ˣ
x = ㏒₅2
Since the x-intercept of f(x) = 1/5 and the x- intercept of g(x) = ㏒₅2. So, they do not have a common x - intercept.
So, the statement d. Both f(x) and g(x) have the same x-intercept of (1, 0) is false.
So, only statement c is true
2. How to find the solution of 3y² + 5y > -2?3y² + 5y > -2
3y² + 5y + 2 > 0
3y² + 3y + 2y + 2 > 0
3y(y + 1) + 2(y + 1) > 0
(3y + 2)(y + 1) > 0
So, the boundary values are at
(3y + 2)(y + 1) = 0
(3y + 2) = 0 or (y + 1) = 0
y = -2/3 or y = -1
So, we require (3y + 2)(y + 1) > 0
For y < -1 say -2, (3y + 2)(y + 1) = (3(-2) + 2)((-2) + 1)
= (-6 + 2)(-2 + 1)
= -4(-1)
= 4 > 0
For -1 < y < -2/3 say -1/3, (3y + 2)(y + 1) = (3(-1/3) + 2)((-1/3) + 1)
= (-1 + 2)(-1 +3)/2
= 1(-2/2)
= -1 < 0
For y > -2/3 say 0, (3y + 2)(y + 1) = (3(0) + 2)((0) + 1)
= (0 + 2)(0 + 1)
= 2(1)
= 2 > 0
So, for (3y + 2)(y + 1) > 0, y < -1 or y > -2/3
So, the solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds
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Answer:
1. D. Both f(x) and g(x) have the same x-intercept of (1, 0).
2. A. x < –1 or x is greater than negative two thirds
Step-by-step explanation:
I took the exam
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) = 8; = 2 P(7 ≤ x ≤ 11)
Using the normal distribution, the indicated probability is given as follows:
P(7 ≤ x ≤ 11) = 0.6247.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 8, \sigma = 2[/tex]
P(7 ≤ x ≤ 11) is the p-value of Z when X = 11 subtracted by the p-value of Z when X = 7, hence:
X = 11:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (11 - 8)/2
Z = 1.5
Z = 1.5 has a p-value of 0.9332.
X = 7:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (7- 8)/2
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
0.9332 - 0.3085 = 0.6247.
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One angle of a triangle is 30° more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.
Answer: [tex]\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}[/tex]
Step-by-step explanation:
Let the smallest angle be x.
Then, the middle angle is x+30.
The largest angle is 2x+30.
Angles in a triangle add to 180 degrees, so:
[tex]x+x+30+2x+30=180\\\\4x+60=180\\\\4x=120\\\\x=30[/tex]
So, the angles measure [tex]\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}[/tex]
The measures of all three angles are 30°,60°, and 90°.
What is meant by triangle?A triangle is a 3-sided polygon occasionally (though not frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which may be the same.
Find the measures of all three angles:
The three angles be a, b and c.
Angle “a" = x
Angle “b" = x + 30°
Angle “c" = “a" + “b"
= x + x + 30°
= 2x + 30°
Total angle in a triangle = 180°
Therefore;
“a" + “b" + “c" = 180°
Births; (x + (x + 30°) + (2x + 30°)) = 180°
So,
4x + 60° = 180°
x = (180° - 60°) ÷ 4
x = 30°
Plugging this value of x into the earlier equations for angles “a,” “b,” and “c."
“a" = x = 30°
“b" = x + 30° = 60°
“c" = 2x + 30° = 90°
The measures of all three angles are 30°,60°, and 90°.
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write the equations after translating the graph of y=|x+2| one unit to the right
write the equations after translating the graph of y=|x+2| one unit to the left
One positive integer is 5 less than twice another. The sum of their squares is 130. Find the integers.
Answer:
7, 9
Step-by-step explanation:
Let x and y represent the two positive integers.
We can write x in terms of y. The question states "one positive integer is 5 less than twice another". Let "one positive integer" represent x.
Therefore:
[tex]x=2y-5[/tex]
We also know that the sum of the squares of the two positive integers is 130. Using this information, we can write another equation.
[tex]x^2+y^2=130[/tex]
These two equations form a system of equations.
[tex]x=2y-5[/tex]
[tex]x^2+y^2=130[/tex]
We can solve this system of equations by the substitution method. Using this method, we substitute [tex]2y-5[/tex] for [tex]x[/tex].
[tex](2y-5)^2+y^2=130[/tex]
Expand [tex](2y-5)^2[/tex] . Notice that [tex](a-b)^2=a^2-2ab+b^2[/tex] :
[tex](2y-5)^2=4y^2-20y+25[/tex]
[tex]4y^2+y^2-20y+25=130[/tex]
Subtract 25 from both sides
[tex]4y^2+y^2-20y=105[/tex]
Add like terms
[tex]5y^2-20y=105[/tex]
Divide both sides by 5
[tex]y^2-4y=21[/tex]
Subtract 21 from both sides
[tex]y^2-4y-21 = 0[/tex]
Factor the equation
[tex]y^2-7y+3y-21=0\\y(y-7)+3(y-7)=0\\(y-7)(y+3)=0\\y=7\text{ or} \ -3[/tex]
Since the question states that the two integers are positive, one of the integers is 7.
We can use this information to find the other integer.
[tex]x=2y-5\\x=2(7)-5\\x=14-5\\x=9[/tex]
[tex]CHECK:\\x^2+y^2=7^2+9^2=49+81=130 \Rightarrow Correct![/tex]
Therefore the two integers are 7 and 9.
Find the coordinates of the point on the curve y = 2x² - x - 1 at which the gradient is 7
Answer:
See below
Step-by-step explanation:
The derivative of the function is the slope
2x^2 - x -1 take derivative ( f ' )
4x -1 equate to 7
7 = 4x -1
x = 2 sub into the original equation to find y = 5
answer this please tysm
Answer:
scalene
Step-by-step explanation:
hidhihihihihihi
Dante is a software salesman. Let represent his total pay (in dollars). Let represent the number of copies of History is Fun he sells. Suppose that and are related by the equation 2400+120x=y
Considering the given linear function, we have that:
The change for each copy that he sells is of $120.If he sells no copies, he makes $2400.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.His payment for x copies bought is:
y = 120x + 2400.
Hence:
The change for each copy that he sells is of $120, as the slope is of $120.If he sells no copies, he makes $2400, which is the y-intercept.More can be learned about linear functions at https://brainly.com/question/24808124
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She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice cubes?
The glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y = -29.202x + 293.5.
In the question, we are informed that the equation of the line of best fit, for the, scatter plot with x representing the number of ice cubes and y representing the milliliters of juice is given as y = -29.202x + 293.5.
We are asked to tell how many milliliters of juice will be in a glass with 7 ice cubes based on the line of best fit.
To find the milliliters of juice in the glass with 7 ice cubes, we substitute x = 7, in the equation of the line of best fit, to get a value of y, representing the milliliters of juice in the glass.
Thus,
y = -29.202x + 293.5,
or, y = -29.202(7) + 293.5 {Substituting x = 7},
or, y = -204.414 + 293.5,
or, y = 89.086.
Thus, the glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y = -29.202x + 293.5.
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Scenario 2 You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount.
The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.
What is the equivalent of the 20% tip as indicated in the task content?The percentage represented as; 20% can be expressed as a fraction.
This follows from the fact that the percentage, % symbol translates to divided by 100.
Consequently, we must note that the 20% translates to; 20/100 = 1/5.
Hence, the 20% tip is one-fifth of the total amount.
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Consider the statements below. Which are propositions? Mark all that apply.
2+2=7
A giant spider with hairy legs.
There are more men than women at BYU-Idaho.
2+2=4
There are more women than men at BYU-Idaho.
Ron hates spiders.
Are you tired today?
The following statements are considered to be propositions:
2 + 2 = 7There are more men than women at BYU-Idaho.2 + 2 = 4Ron hates spiders.What is deductive reasoning?Deductive reasoning can be defined as a type of logical reasoning that typically involves drawing conclusions based on a given set of rules and conditions or from one or more premises (factual statements) that are assumed to be generally (universally) true.
What is a proposition?A proposition can be defined as a type of statement (assertion) that is typically used to express an opinion or a judgement, with either a true or false answer.
This ultimately implies that, a proposition refers to a type of statement (assertion) that is either a true or false.
In this context, we can infer and logically deduce that the following statements are considered to be propositions:
2 + 2 = 7There are more men than women at BYU-Idaho.2 + 2 = 4Ron hates spiders.Read more on propositions here: https://brainly.com/question/24158168
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Which inequality is represented by the following graph?
x ≤ 4
Answer:
X is less than and equal to 4
30% of what number is
165
Answer:
550
Step-by-step explanation:
165 x 100= 16500/30=550
If Peter pays $84 to buy a watch after discount of 20% find the original price of the watch
Answer: 105 dollars
Step-by-step explanation:
Let's say that the original price x dollars, we can use the equation to find the original price.
80%x = 84
x = 105
Answer:
$105
Step-by-step explanation:
The multiplier is 0.8
To get the price after the discount,the original price was multiplied by 0.8(100 - 20 = 80% = 0.8
Therefore to obtain the original price from the price after the discount, we use reverse percentage:
$84 ÷ 0.8 = $105
What is the center and radius of the circle?
USH financial is a small bank that is examining its customers use of its website.the number of online transactions made per day during the past 9 days are as follows
The mean, median, and mode are;
median=77
Mean=73.33
Mode= 78, 67
This is further explained below.
What is median?Generally, The middle number in a list that is arranged from smallest to greatest is referred to as the median. On the list, the value that occurs most often is known as the mode. Therefore
median=77
Generally, In mathematics, particularly statistics, the term "mean" may refer to a number of different concepts. The purpose of each mean is to summarize a certain collection of data, often for the purpose of gaining a better understanding of the overall value of a specific data set.
A dataset's mean (also known as the arithmetic mean, which is distinct from the geometric mean) is calculated by dividing the sum of all of the values in the dataset by the total number of values in the dataset. It is the measure of central tendency that is used the most often, and it is sometimes referred to as the "average."
[tex]mean=\frac{\sum x}{n}\\\\Mean=\frac{78+67+98+50+67+78+67+77+78}{9}[/tex]
Mean=73.33
Mean=73.3 in one dp
What exactly is the mode in math?In conclusion, The mode is the number that appears the most often, or the number that stands out as having the most occurrences overall. The number 2 is the mode of the sequence 4, 2, 4, 3, 2, 2 because it appears three times, which is more than any other number in the sequence.
The mode of 78, 67, 98, 50, 67, 78, 67, 77, 78 is
Mode= 78, 67
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
What is a Chord in Geometry?In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.
What is the Congruent Chords Theorem?In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.
In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.
According to the congruent chords theorem, NS = PS, thus:
8 = 2x - 6
8 + 6 = 2x
14 = 2x
Divide both sides by 2
14/2 = 2x/2
7 = x
x = 7
LP = 1/2(12)
LP = 6 units.
In summary, applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
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35. Calculate the area of ARST if b = 29.
R
S
30°
1456.65 units²
841 units²
728.33 units²
364.16 units²
b
T
None of these answers are correct.
The area based on the information illustrated will be 825 unit².
How to illustrate the information?Your information is incomplete. Therefore, an overview will be given. It should be noted that area simply means the quantity which expresses the extent of the region on a plane as well as a curved surface. Based on this information, it should be noted that the area of a rectangle is given as:
Area = Length × Width
Let's assume that the width is 25 units and the length is given as 33 units.
Then, the area will be:
= Length × Width
= 33 × 25
= 825 units²
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Which of the following shows one way to simplify 43Σn=1(3+9n)?
Based on the given summation notation, the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n
How to determine the summation expression?The expression is given as:
43Σn=1(3+9n)
As a general rule, if a summation notation is represented using the following expression
Σ(a + bn)
The equivalent expression of the above summation notation is
Σa + bn
Where the variable a is a constant in the expression
This means that:
Σ(a + bn) = Σa + bn
Using the above equation as a guide, we have the following equivalent equation
43 Σ n=1 (3+9n) = 43 Σ n=1 3 + 43 Σ n=1 9n
Hence, based on the given summation notation; the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n
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Answer:
D on 3dg I took the best
Step-by-step explanation:
2. What are the outliers for: 19, 2, 4, 5, 7, 3, 1, 3, 20
A two digit number has 6 more ones than tens. Twice the sum of the number and its reverse is 6 more than ten times the number. Find the number.
The number with the given characteristics is 17
How to determine the numbers?Let the tens be x and the units be y.
So, the number is 10x + y
The relationship between the digits is
y = x + 6
The relationship between the number and the reverse is
2(10x + y + 10y + x) = 6 + 10 * (10x + y)
Simplify the second equation
2(11x + 11y) = 6 + 100x + 10y
Open the brackets
22x + 22y = 6 + 100x + 10y
Substitute y = x + 6
22x + 22(x + 6) = 6 + 100x + 10(x + 6)
Expand
22x + 22x + 132 = 6 + 100x + 10x + 60
Collect like terms
22x + 22x - 100x - 10x = 6 + 60 - 132
Evaluate the like terms
-66x = -66
Divide by -66
x = 1
Substitute x = 1 in y = x + 6
y = 1 + 6
y = 7
Recall that the number is 10x + y
So, we have
Number = 10 * 1 + 7
Evaluate
Number = 17
Hence, the number is 17
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which equation shows that the Pythagorean identity is true for 0 = 180 degrees? select the equation that is in the form sin^2 0+cos^2 0=1
A. 0^2 + (-1)^2 = 1
B. 1^2 + 0^2 = 1
C. 0^2 + 1^2 = 1
D. (-1)^2 + 0^2 = 1
The equation in the form of the given expression is (0)² + (1)² = 1
Trigonometry identityAccording to some of the trigonometry identity
sin 0 = 0
cos 0 1
Given the expression below
sin^2 0+cos^2 0=1
This can also be expressed as:
(sin0)² + (cos0)² = 1
Substitute
(0)² + (1)² = 1
Hence the equation in the form of the given expression is (0)² + (1)² = 1
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Number #2 please, I don’t know how to solve it.
Answer:
See below
Step-by-step explanation:
Here is HOW to solve this problem:
b = pounds of blue candy then r = 11-b = pounds of red candy
.79b = cost of blue candy 1.29 (11-b) = cost of red candy
these two costs sum to 11.19
.79b + 1.29 ( 11-b) = 11.19 Now you can solve for 'b' the 'r' = 11-b
Answer:
Red candy =5
Blue candy = 6
Step-by-step explanation:
Let the pounds of red candy be x and blue candy y. Then y=11-x
Also 1.29x + 0.79y=11.19
1.29x+0.79(11-x)=11.19
0.5x=11.19–8.69
0.5x=2.5
X=5
Red candy =5
Blue candy = 6
A troupe of 12 dancers is going to line up on stage. Of these dancers, 6 are wearing green and 6 are wearing blue. A dancer wearing green must be in the first position and they must alternate between colors. In how many ways can the dancers line up?
The number of ways that the dancers can line up is; 518400 ways
What is the Fundamental Counting Theorem?The fundamental counting theorem is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
N = n1 * n2 * n3.....*nₙ
Total = 12
Dancers on Green = 6
Dancers on blue = 6
Number of ways for those wearing green = 6!
Dancers wearing green must be in the first position and so 6 places are left for the blue dancers.
Number of ways to arrange those wearing blue = 6!
Thus;
Number of ways that the dancers can line up = 6! * 6! = 518400 ways
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What are the next three terms in the sequence -27, -19,
-11, -3, 5, ...?
Answer:
13, 21, 29
Step-by-step explanation:
You are adding 8 to each term. -27 + 8 = -19 + 8 = -11 + 8 = -3, etc.
A pet store has 5 puppies, including 2 poodles, 2 terriers, and 1 retriever. Rebecka and Aaron, in that order, each select one puppy at random without replacement. Find the probability that Aaron
selects a retriever, given Rebecka selects a retriever.
The probability is
(Type an integer or a simplified fraction.)
Answer:
1/4
Step-by-step explanation:
Rebecka already chose a retriever, so the puppies left for Aaron to pick are:
2 poodles
2 terriers
1 retriever
Total: 4
Number of retrievers left after Rebecka's pick: 1
p(Aaron picks retriever) = 1/4
Cannington, Inc., designs, manufactures, and markets personal computers and related software. The following information was taken from a recent annual report of Cannington industries: Property, Plant, and Equipment (in millions): Current Year Preceding Year Land and buildings $707,150 $410,147 Machinery, equipment, and internal-use software 671,793 530,363 Office furniture and equipment 106,073 91,930 Other fixed assets related to leases 855,652 643,507 Accumulated depreciation and amortization (898,081) (749,579) a. Compute the book value of the fixed assets for the current year and the preceding year. Current year book value $fill in the blank 1 Preceding year book value $fill in the blank 2
The book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.
Book valueCurrent year book value
Land and buildings $707,150
Machinery, equipment, and internal-use software $671,793
Office furniture and equipment $106,073
Other fixed assets related to leases $855,652
Less Accumulated depreciation and amortization ($898,081)
Book value $1,442,587
Preceding year book value
Land and buildings $410,147
Machinery, equipment, and internal-use software $530,363
Office furniture and equipment $91,930
Other fixed assets related to leases $643,507
Less Accumulated depreciation and amortization ($749,579)
Book value $926,368
Therefore the book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.
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HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT
BE ZERO AND:
1) THE TELEPHONE NUMBER MUST BE A MULTIPLE OF 100?
2) ONLY ODD DIGITS CAN BE USED?
3) THE FIRST 3 DIGITS ARE 277?
Answer:
there are 8 million different phone numbers whose phone numbers whose digits aren't 0 or 1
Graph the polar equation r=1-3 sin 0
No graph for the polar equation because here sin 0 is 0.
According to the statement
we have given that a polar equation and we have to represent in the graph.
So, For this purpose, we know that the
The expression of a point as an ordered pair. is known as polar notation, the equation of a curve expressed in polar coordinates is known as a polar equation.
The given polar equation is
r = 1-3 sin 0
here the value of r is 0.
so, No graph is possible for the given statement
because here the value of r is 0 and for zero value there is a no graph possible.
So, No graph for the polar equation because here sin 0 is 0.
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Look at the way this plane figure moved. Which set of transformations was performed? Help me please it's urgent!
A) reflect horizontally and reflect vertically
B) reflect vertically and rotate clockwise
C) translate right and rotate counter-clockwise
Using translation concepts, the set of transformations that was performed on the triangle are given as follows:
A) reflect horizontally and reflect vertically.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the orientations of the triangle changed both horizontally and vertically, with no change in the format, hence there were reflections, which means that the correct option is:
A) reflect horizontally and reflect vertically.
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one of the angles of a triangle is 106° and the other two angles are equal find each of the equal angles
Answer:
37°
Step-by-step explanation:
• recall that the sum of the interior angles of a triangle
is equal to 180°
Then
The measure of the two other angles :
= 180 - 106
= 74°
The measure of each of the equal angles :
= 74 ÷ 2
= 37°
Answer:
the 2 angles r 37
Step-by-step explanation:
the angles of triangle sums up to 180, and lets call the unknown angle x, since they're both equal, x+x=2x
so when 3 angles of triangle adds up, we get 180
106+2x=180
2x=180-106
2x=74, divide both sides by 2 to get x
x=74/2
x=37
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