The range of the function g, given the premises for f(x) = |x| and a < 0 while b ≠ 0 is; the set of all real numbers.
Range of a functionIt follows from the task content that the range of the function g(x) = a|x| + b is to be determined given the parameters as in the task content.
Since the function f(x) = |x| has a range of y ≥ 0, and a is a negative number ( < 0), it therefore means that the a|x| is always a number less than 0 (<0).
However, the possible values of constant, b include all real numbers except 0.
On this note, the function g(x) = a|x| + b has a range which is the set of all real numbers. This is so because, g(x) > 0 when a|x| < b and g(x) < 0 when a|x| > b.
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A car originally is worth $3000. It is decreasing in value by 3% every year. How much is it worth in 3 years.
(Round to the nearest cent)
Answer:
$2825,32
Step-by-step explanation:
Value of the car after 1 year
$3000 * 3% = 3000 * 0.03 = 90
3000 - 90 = $2910
Value of the car after 2 year
$2910 * 3% = 2910 * 0.03 = 87.3
2910 - 87.3 = $2912,7
Value of the car after 3 year
$2912,7 * 3% = 2912,7 * 0.03 = 87.381
2912,7 - 87.381 = $2825,319
"Round to the nearest cent"
$2825,32
very stuck please help
The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
In the question ,
it is given that
the required line is perpendicular to the line passing through (6, -2) and (-8 ,5) .
the slope is = (5 -(-2))/(-8 -6)
= 7/(-14)
= -1/2
so , the slope of the required line is = 2 .
The equation of the line passing through the point (3,1) with slope 2 is
(y - 1) = 2*(x-3)
y -1 = 2x - 6
y = 2x - 6 + 1
y = 2x - 5
the equation of line is y [tex]=[/tex] 2x - 5
the perpendicular slope is = 2
the y intercept is -5 .
Therefore , The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
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Select the correct answer. Which expression is equivalent to , if x ≠ 0 and y ≠ 0? A. B. C. D.
see image below:
The expression similar to [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex] obtained by using the laws of indices is option A.
A. [tex]2\cdot x^2 \cdot y\sqrt[3]{7\cdot x \cdot y^2}[/tex]
What are the laws of indices?According to some of the laws of indices, we have;
[tex]\dfrac{1}{x^n} =x^{-n}[/tex]
[tex]x^m \cdot x^n = x^{m+n}[/tex]
[tex]\sqrt[m]{x^n} =x^{\frac{n}{m} }[/tex]
The expression can be presented as follows; [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]
Simplifying the above expression gives;
[tex]\sqrt[3]{56\cdot x^7\cdot y^5 } = \sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]
[tex]\sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]
Collecting terms with an index of a multiple of 3 gives;
[tex]\sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 }[/tex]
[tex]\sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 } = 2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]
The expression that is equivalent to [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]is option A.
A. [tex]2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]
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suppose 44% of politicians are lawyers. if a random sample of size 853 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 40%? round your answer to four decimal places.
The probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .
Given :
Population Proportion ( p ) = ( 44 % ) = 0.44
Sample proportion ( p hat ) = ( 40 % ) = 0.4
Size of sample ( n ) = 853
To find : P ( p hat < 0.4 )
Formula : ( p hat - p ) / [tex]\sqrt{ p * ( 1 - p ) / n }[/tex]
Substituting values in the above formula ,
z = ( 0.4 - 0.44 ) / [tex]\sqrt{ 0.44 * ( 1 - 0.44 ) / 853}[/tex]
z = - 2.3535
z - score = -2.3535
Finding the p - value :
p - value = 0.009299
Therefore , the probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .
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The population of a state was estimated to be
about 38,332,521 people. Write the estimated
population as a single digit times a power of 10.
The state population as a single-digit time power of 10 is approximately 4 × 10⁷.
What is estimation?Calculations are made easier and more realistic when a number is estimated, which is a plausible estimation of its true value.
To estimate something is to approximate it as accurately as possible.
To acquire a quick and approximate response is obtained by rounding down the values used in the computation.
Given the state estimated population = 38,332,521
Divide and multiply by 10
So,
= 3,833,252.1 × 10¹
= 383,325.21 × 10²
So, similarly, we can write
= 3.8332521 × 10⁷
So, we can write the state population as approximately 4 × 10⁷
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How to subtract 27 minus 9.9 using mental math
Answer: you are left with 17.1 or 17.10
HOW TO: picture this. i'ma going to go to your store and you have 27 dollars. you owe me 9.90 for some reason. you give me the money and i go on my way. how much money are you left with?
question 1 a sample random sample of 6 bulbs was selected from a lot of 100 for the purpose of estimating its quality. the life of each bulb selected was measured by letting the bulb until it burned out. the results from the test are as follows: bulb number life duration (hours) 1 950 2 1210 3 1070 4 840 5 1420 6 980 a.) estimate the average life of the bulbs in the lot. b.) estimate the total life bulbs in the lot c.) estimate the proportion of bulbs in the lot with life exceeding 1000 d.) estimate the number of bulbs in the lot with life exceeding 1000
a) The average life of the lot is 1078.33 hrs, b) the total life is 107833.33 hours, c) a proportion of 1/2 bulbs have a life exceeding 1000 hrs while d) an estimation of 50 bulbs have a life exceeding 1000 hours.
It is given that the number of bulbs in a given lot is 100.
The number of bulbs in the sample selected is 6
The life of the sample bulbs was
no. life (hours)
1 950
2 1210
3 1070
4 840
5 1420
6 980
a)
The average life of the bulbs can be calculated by
the sum of the lives of the sample/ no. of samples
= (950 + 1210 + 1070 + 840 + 1420 + 980) / 6
= 1078.3333 hrs
b) The total lives of the bulbs in the lot will be
average life X no. of bulbs
= 1078.3333 X 100
= 107833.33 hrs
c)
We can gain the proportion of the bulbs that have a life exceeding 1000 hrs by the given sample
The bulbs
2, 3, and 5 have lives exceeding 1000 hrs.
Hence, out of 6 bulbs, 3 have lives exceeding 1000 hrs.
Therefore the proportion
= 3/6
= 1/2
d)
The number of bulbs in the lot with a life exceeding 1000 will be
proportion X no. of bulbs
= 1/2 X 100
= 50 bulbs
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The equation below describes a function of x . y=−4x+12
The solution for x in the function when the equation y=−4x+12 equals -12 is -6
How to determine the solution for x in the function?From the question, we have the following equation that can be used in our computation:
y=−4x+12
To make the equation legible, we need to rewrite it
So, we have the following representation
y = −4x + 12
Also from the question, we have
y = -12
This means that we calculate x when y = -12
Substitute the known values in the above equation, so, we have the following representation
-12 = -4x + 12
So, we have the following equation
-4x + 12 = -12
Add -12 to both sides of the equation
So, we have the following representation
-4x + 12 - 12 = -12 - 12
Evaluate the like terms in the equation
-4x = -24
Divide both sides of the equation by -4
x = 6
Hence, the solution is 6
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Possible question
The equation below describes a function of x . y=−4x+12
Solve for x when y = -12
help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length of the shorter leg is 9 mm.
The length of the longer leg is 12 mm.
The length of the hypotenuse is 15 mm.
Pythagoras theory applies to every right triangle. If
The shorter leg = aThe longer leg = bThe hypotenuse = c[tex]a^2 + b^2 = c^2[/tex]Step-by-step explanation:
Known
Longer leg = shorter leg +3 mmAsked
a?b?c?Answer
[tex]a^2 + b^2 = c^2[/tex]
[tex]a^2 + (a+3)^2 = (a+6)^2[/tex]
[tex]a^2 + a^2 + (2 \times a \times 3) + 3^2 = a^2 + (2 \times a \times 6) + 6^2[/tex]
[tex]2a^2 + 6a + 9 = a^2 + 12a + 36[/tex]
[tex]2a^2 - a^2 + 6a - 12a + 9 - 36 = 0[/tex]
[tex]a^2 - 6a - 27 = 0[/tex]
[tex]a^2 - 9a + 3a - 27 = 0[/tex]
[tex]a \times (a - 9) + 3 \times (a - 9) = 0[/tex]
(a-9) (a+3)=0
a-9=0 or a+3= 0
a=9 or a=-3 (impossible)
Shorter leg
a=9 mm
Longer leg
b = a+3
b = 9+3
b = 12 mm
Hypotenuse
c = a+6
c = 9+6
c = 15 mm
I NEED THIS GRAPH SOLVED ASAP
I need either the function in factored form or the roots(with multiplicity) or standard form thank you and please!!!
Answer:
if the root is 10 then the function is ²✓5
Hi I'm honestly really confused on this problem and have no idea what I'm meant to do. It'd be helpful if someone could explain this
As corresponding angles ∠5 and ∠8 are equal. Hence line x is parallel to line z by converse of corresponding angles theorem.
What does converse of corresponding angles theorem states?
If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
How can we show two lines are parallel to each other?
We can show lines are parallel by finding a pair of corresponding angles that are congruent.
Proving if two lines are parallel then third line is parallel too.
According to the given data:
It is given in the question that line x is parallel to line yTherefore, ∠5 ≅ ∠7 (i.e. corresponding angles)
∠5 = ∠7
Similarly as given line y is parallel to line z∠6 ≅ ∠8 (Corresponding angles are equal)
∴ Measure of angles is also equal ⇒ ∠6 = ∠8
∠5 = ∠8 (transitive property of equality of angles which says if
∠a = ∠b and ∠b = ∠c then ∠a = ∠c)
∠5 ≅ ∠8 (If measure of angles is same then they are congruent)
Therefore, line x || line z
(Converse of the Corresponding Angles Theorem).
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Algebra 2 please help!
Which table of values would produce the graph shown above?
The table (D) values would produce the same graph as shown.
What is a Graph?Mathematical structures known as graphs are used to describe pairwise relationships between things. Graph theory is the study of these mathematical structures. Vertices (also known as nodes or points) and edges are what make up a graph in this sense (also called links or lines). It is possible to distinguish between directed and undirected graphs, where edges connect two vertices asymmetrically and symmetrically, respectively. One of the primary topics in discrete mathematics is graphs.
From the graph, find the intercepts,
At x = 0, the value of y is -1.
At, y = 0, the value of x is 4
So, from the given options, we can see that the values are given in table (D).
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d) The rent of a room for 4 months is Rs 20,000. (i) What is the rent for 7 months? (ii) How long would a tenant hire the room for Rs 55,000 at the same rate of rent?
The rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
The rent of a room for 4 months is Rs 20,000.
The rent of a room for 1 month is Rs 20,000./4
The rent of a room for 1 month is Rs 5000
The rent of a room for 7 months is Rs 5000 x 7
The rent of a room for 7 months is Rs 35000
Now we need to calculate the number of month a tenant hire the room for Rs 55,000 at the same rate of rent
The rent is 5000 for 1 month
The rent will be 55000 for 1/5000 x 55000 = 11 months
Therefore, the rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
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is y=4x-8, continuous or discrete?
The equation y = 4x - 8 is discrete
What are discrete data?Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.
While complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.
The difference between discrete and continuous dataThe main distinction between continuous and discrete data is that the former has a finite value that can be counted while the latter has an endless number of possible values that can be measured.
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y = 1,000x is that a constant proportionality
In a company, 85% of the workers are women. If 675 people work for the company who aren't women, how many workers are there in all?
Answer:
so there are 3825 worker in total
Step-by-step explanation:
675=15%
women=85%
how much workers are 5%=675/3 =225
225=5%
how many workers is 85%= 85/5=17
85%=225x17=3825
What is the equation in standard form of the line that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y=1
The required equation of line in standard form that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y = 1 is
y = (3/8)x - 13/4
How to find equation of line if one point and equation of perpendicular line is given?
To find the equation of line which is perpendicular to another line
Find slope of the required line using m₁. m₂ = -1Using the given point find y-intercept by substituting in the equation of line.According to the given question:
Let the required equation of line be y = mx + b
where m is the slope of line and b is the y-intercept
Now, 8x + 3y = 1 is perpendicular to the line. Hence, the slopes of both line will satisfy m₁. m₂ = -1
Standard form of the given line is
y = (-8/3)x + 1/3
∴ m₁ = -8/3
Finding m₂, (-8/3). m₂ = -1
∴ m₂ = 3/8 ------ (1)
Using the given point (6, -1) to find y-intercept in the equation
y = (3/8)x + b
-1 = (3/8)(6) + b
∴ b = -13/4
Therefore the required equation of line in standard form is
y = (3/8)x - 13/4
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What is the zero of g?
(-6,0)
(-3, -4.5)
(-8, 0)
(0,-9)
Answer: Either C. or D.But I'm sure it's D.
Step-by-step explanation:
2.8x + 10 + 5.7x = 70+x
Answer:
Step-by-step explanation a=0.32
The required simplified value of x in the given expression is 8.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
2.8x + 10 + 5.7x = 70+x
Simplifying,
8.5x + 10 = 70 + x
8.5x - x = 70 - 10
7.5x = 60
x = 60 / 7.5
x = 8
Thus, the required simplified value of x in the given expression is 8.
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find the inequality 2x/3 <4
Answer:
x<6
Step-by-step explanation:
2x/3<4
2x<12
x<6
Answer:
x < 6
Step-by-step explanation:
[tex]\frac{2x}{3}[/tex] < 4 ( multiply both sides by 3 to clear the fraction )
2x < 12 ( divide both sides by 2 )
x < 6
rationalise the denominator [tex]\frac{1}{4-\sqrt-{11} }[/tex]
Answer:
[tex]\frac{4+\sqrt{11} }{5}[/tex]
Step-by-step explanation:
to rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.
the conjugate of 4 - [tex]\sqrt{11}[/tex] is 4 + [tex]\sqrt{11}[/tex] , then
[tex]\frac{1(4+\sqrt{11}) }{(4-\sqrt{11})(4+\sqrt{11}) }[/tex] ← expand denominator using FOIL
= [tex]\frac{4+\sqrt{11} }{16-11}[/tex]
= [tex]\frac{4+\sqrt{11} }{5}[/tex]
please help fast algebra 2
Find m∠1 and m∠2. Tell which theorem can be used.
According to the vertical angles theorem, m∠1 = 117°.
Based on the corresponding angles theorem, m∠2 = 117°.
What is the Vertical Angles Theorem?The set of angle pairs formed that are directly opposite each other when two straight lines intersect or when two parallel lines are crossed by a transversal are said to be vertical angles, and therefore congruent to each other based on the vertical angles theorem.
What is the Corresponding Angles Theorem?When two lines are intersected by a transversal, the angles that are on the same transversal and lie in relative position or corner in the two parallel lines are said to be corresponding angles which are congruent based on the corresponding angles theorem.
Using the information given in the diagram attached below, angles 1 and 117° are vertical angles.
Therefore:
m∠1 = 117° [vertical angles theorem]
Angles 1 and 2 are corresponding angles. Therefore:
m∠2 = m∠1
Substitute
m∠2 = 117° [corresponding angles theorem]
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twelve fair dice are rolled. what is the probability that the product of the numbers on the top faces is prime?
Probability that the product of the numbers on the top faces is prime is 1/2(1/6)⁴.
Define probability.In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution. Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.
Given,
12 fair dice rolled,
Probability that the product of the numbers on the top faces is prime:
⁶C₅ × (1/6)⁵ × ³C₁/⁶C₁
6 × (1/6)⁵ × 3/6
1/2(1/6)⁴
Probability that the product of the numbers on the top faces is prime is 1/2(1/6)⁴.
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two trains leave a station at the same time and travel in opposite directions. one train travels 20 kph faster than the other train. after 3 hours, they are 810 miles apart. what is the speed of each train?
The speed of each train is 125kph and 145kph.
Here it is given that the distance between the two trains is 810 miles after traveling for 3 hours.
The difference in their speed is 20 kph.
Let x be the speed of one train. So by this, we get the speed of the second train that is x + 20.
Formula to calculate speed is:
Speed = Distance / Time
Distance = Speed × Time
Distance covered by first train = x × 3
Distance covered by second train = (x + 20) × 3
Total distance = 810
So we get;
3x + (x + 20)3 = 810
3x + 3x + 60 = 810
6x = 750
x = 125
x + 20 = 125 + 20 = 145
Therefore we get the speed of both trains which is 125kpp and 145 kph.
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The wholesale cost for a purse in a department store is $12. 50. The store plans to mark up the purse by 140%. What will be the selling price of
the purse to the nearest cent?
Give me the right anwser
The selling price of the the purse in a department store is cents.
Define the term selling price?A product's or service's selling price is the seller's final price, or how much the buyer pays for anything. The trade can be for a certain proportion, quantity, or measure of a commodity or service.The price at which you sell anything must be sufficient to generate a profit. It must also establish a market position.For the given question-
A purse in such a department store costs $12.50 at wholesale.
The purse will be 140% more expensive at the store.
Then,
140% of 12.50 = 140 x 12.50 / 100
140% of 12.50 = 17.5
Selling price = percent increase + cost price
Selling price = 17.5 + 12.5
Selling price = $30.0
Selling price = 3000 cents
Thus, the selling price of the the purse in a department store is cents.
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You go out to eat with 3 friends and your meal was $72.50. There is 6.75% sales tax and you plan to tip the server 15%. How much should each person pay?
The amount that each person should pay is $22.06 .
in the question ,
it is given that
total number of persons = 3 person + 1 = 4 persons
cost of the meal = $72.50
sales tax percent = 6.75%
tip percent = 15%
So , the amount of sales tax = 6.75% of cost = 0.0675 * 72.50 = $4.89
and , the amount of tip is = 15% of cost
= 0.15 * 72.50
= 10.87
So , the total amount payable is = cost + sales tax + tip
= 72.50 + 4.89 + 10.87
= 88.26
since the total number of persons is 4 ,
the amount per person is = 88.26/4 = 22.06
Therefore , The amount that each person should pay is $22.06 .
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PLEASE HELP!! WILL GIVE BRAINLIEST
The mass of a test sample is 10g, and it has the volume of 2.5cm^3 . What is its density?
A. 10g/cm^3
B. 2.5cm^3/g
C. 4g/cm^3
D. 4cm^3/g
E. 0.25g/cm^3
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
Define density.The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.
Given,
Volume = 2.5 cm³
Mass = 10 g
For density:
Mass ÷ volume
10 ÷ 2.5
4
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
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The local craft fair charges the vendors a flat rate of $15 plus $10 for each hour that they splend at the fair. If the vendor owed $65, how many hours did he remain at the craft fair?
Answer:
5 hours
Step-by-step explanation:
$65 - $15 = $50
$50/$10 = 5
A runner completed a 26.2-mile
marathon in 210 minutes.
a. Estimate the unit rate, in miles per minute.
b. Estimate the unit rate, in minutes per mile.
c. Another runner says, “I averaged 10-minute miles in the
marathon.” Is this runner talking about the unit rate
described in part (a) or in part (b)? Explain your reasoning.
Step-by-step explanation:
The answer is: A=210÷26.2=8.2
B=now we have to turn minutes in to haurs 210:60=3.5 now 26.2÷3.5=29.7
Answer:
A) 26.2/210= .125 miles per minute
B) 210/26.2= 8.02 minutes per mile
C) the other runner talks about the same rate as b), not a).
Step-by-step explanation:
A)[tex]\frac{26.2}{210\\}[/tex] and B)[tex]\frac{210}{26.2}[/tex] :)
C)the runner was referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.
If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.