Linear functions are those whose graph is a straight line and it has the following form. y = f(x) = a + bx.
There are several ways to represent a linear function such ad word form, function notation, tabular form, and graphical form.
The key features of a linear function identified and interpreted from a description as an increasing linear function results in a graph that slants upward from left to right and has a positive slope.
What is a linear function?A linear function can be expressed as a point slope or a line with a slope intercept. The ordered pairs will represent points on the line where a table of values representing the function is provided. According to the values in the table, the gradient of the line is a ratio of rise to run. The gradient and initial value of the function are shown in slope intercept form.
A graph with a positive slope and a left-to-right slope is produced by an increasing linear function. A graph with a negative slope and a left-to-right slant is produced by a decreasing linear function. A graph with a constant linear function looks like a horizontal line.
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Please help! I need the answers and work for them, please and thank you!
Answer:
We can solve this problem by using the information provided in the riddle to create a system of equations. Let x be the number of pencils that were originally in the box. We can then create the following equations:
x < 40
x - 4 = 2
x - 3 = 0
x - 5 = 0
We can then solve this system of equations to find the value of x. First, we note that the second and third equations imply that x is equal to 3 or 5. Substituting these values into the first equation, we find that x cannot be 3, as this would violate the inequality. However, x can be 5, as 5 is less than 40. Therefore, the number of pencils that were originally in the box is 5.
Find the Area of the figure below, composed of a rectangle and a semicircle. The radius of the circle is shown. Round to the nearest tenths place.
Answer:
13 × 10 = 130 ( it's a rectangle)
5² π /2 ≈ 12.5 × 3.14 = 39.25 ( semicircle)
130 + 39.25 = 169.25 ≈ 170
Imagine tossing a fair coin 4 times give a probability for this chance process
B define event b as getting exactly three tails find P(B)
This can be solved by Binomial Probability Distribution Method.
By solving we get P(B) = 0.25.
What is Binomial Probability Distribution?The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.
P(X=x)=Cₙ.ₓ×p^x×(1-p)^(n-x)
Cₙ,ₓ=[tex]\frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.Explanation:Case 1:
The coin is tossed 4 times, hence n=4
It is a fair coin, so it has equal number of chances for heads and tails. So P(a)=0.5
Case2:
P(B) is P(X=3),hence:
P(X=x)=Cₙ.ₓ×p^x×(1-p)^(n-x)
⇒P(X=3)=C₄,₃×(0.5)^3×(0.5)^(1)
⇒P(X=3)=0.25
This can be solved by Binomial Probability Distribution Method.
By solving we get P(B) = 0.25.
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This can be solved by Binomial Probability Distribution Method.
By solving we get P(B) = 0.25.
What is Binomial Probability Distribution?The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.
P(X=x)=Cₙ.ₓ×p^x×(1-p)^(n-x)
Cₙ,ₓ= [tex]\frac{n!}{x!(n-x)!}[/tex]
The parameters are:
• x is the number of successes.
• n is the number of trials.
• p is the probability of a success on a single trial.
Explanation:Case 1:
The coin is tossed 4 times, hence n=4
It is a fair coin, so it has equal number of chances for heads and tails. So P(a)=0.5
Case2:
P(B) is P(X=3),hence:
P(X=x)=Cₙ.ₓ×p^x×(1-p)^(n-x)
⇒P(X=3)=C₄,₃×(0.5)^3×(0.5)^(1)
⇒P(X=3)=0.25
This can be solved by Binomial Probability Distribution Method.
By solving we get P(B) = 0.25.
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What does the word amphibian come from? like amphi comes from the word ** and Brian comes from the word **
Answer:
The word amphibian is a Greek word. It is the combination of the world “amphi,” which means dual, or both kinds and the word “bio,” which means life.
Step-by-step explanation:
The name amphibian, derived from the Greek amphibios meaning “living a double life,” reflects this dual life strategy—though some species are permanent land dwellers, while other species have a completely aquatic mode of existence. Approximately 8,100 species of living amphibians are known.
Find the volume of question number 14
Answer:
5494.5
Step-by-step explanation:
[tex]\frac{1}{3}(37)(33)(13.5)=5494.5[/tex]
Two friends, Nayeli and Aiden, had just bought their first cars. The equation y=22.8xy=22.8x represents the number of miles, yy, that Nayeli can drive her car for every xx gallons of gas. Aiden uses 5 gallons of gas to drive 210 miles in his car.
How many miles less does Nayeli's car travel on one gallon of gas than Aiden's car?
Answer:
Step-by-step explanation:
Use the form
a
cos
(
b
x
−
c
)
+
d
to find the amplitude, period, phase shift, and vertical shift.
show that f is continuous on (−[infinity], [infinity]). f(x) = 1 − x2 if x ≤ 1 ln(x) if x > 1
The function f is continuous on (-∞, ∞).
What are Continuous Functions?A function f is said to be continuous at a point 'a' if,
lim ₓ→a f(x) = f(a).
f(x) = [tex]\left \{ {{1-x^2 if x\leq 1} \atop {ln x if x > 1}} \right.[/tex]
That is, if x ≤ 1, f(x) = 1 - x² and if x > 1, f(x) = ㏑ x
Taking interval (-∞, 1], f(x) is a polynomial 1 - x².
Polynomials are continuous everywhere. So f is continuous at (-∞, 1].
Now take the interval (1, ∞).
[tex]\lim_{x \to \infty} f(x)[/tex] = [tex]\lim_{x \to \infty} lnx[/tex] = ㏑ ∞ = ∞ = f(∞)
So f is continuous at the interval (1, ∞)
To check for continuity at 1,
lim x → 1⁻ f(x) = lim x → 1⁻ [1 - x²] = 1 - 1² = 0
lim x → 1⁺ f(x) = lim x → 1⁺ ㏑ x = ㏑ 1 = 0
So, lim x → 1⁻ f(x) = lim x → 1⁺ f(x)
So f is continuous in the whole interval (-∞, ∞).
Hence the function f(x) = [tex]\left \{ {{1-x^2 if x\leq 1} \atop {ln x if x > 1}} \right.[/tex] is continuous on the interval (-∞, ∞).
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Simplify.
Sqrt • 100
Answer: 10
Step-by-step explanation:
10 times 10 = 100
So square root of 100 = 10
10pts and whoever gets this right gets brainliest✅️
Answer:
Step-by-step explanation:
Your second option is your answer;
Arrow pointing to the right with circle filled. Your arrow would start at the 2.
I the ytem of equation conitent and independent conitent and dependent or inconitent
Y=-x1
2y=-2x2
The system of linear equations, y = -x + 1 ; 2y = -2x + 2 has infinite many solutions so it is dependent Consistent .
What is dependent Consistent system ?A system of linear equations consists a pair of equations with same variable. An ordered pair that satisfies all equations of the system is the solution of the system. A linear system of equations is consistently dependent if there are infinitely many solutions. In this case, the system line graph is the same. That is, the equations for the system represent the same line. We have System of equations ,
y = -x + 1 => x + y -1 = 0--(1)
2y = -2x + 2 => 2x + 2y -2 = 0 --(2)
Comparing the equation (1) with standard equation a₁x + b₁y + c₁z = 0 and equation (2) with
a₂x + b₂y + c₂z = 0 , we get
a₁ = 1 , b₁ = 1 , c₁ = -1 , a₂ = 2 , b₂ = 2 , c₂= -2
Now, we check the ratio of coefficients
a₁/a₂ = 1/2 , b₁/b₂= 1/2 , c₁/c₂= -1/-2 = 1/2
=> a₁/a₂ = b₁/b₂= c₁ /c₂
Thus, the lines are coincide with each other then there exist infinite number of solutions since, a line has infinite points. In such a case, the pair of lines is said to be dependent and consistent. Therefore, system of equations is dependent and consistent.
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What is the coefficient of the x¹y³ term in the expansion of (x - 2y)'?
X
-8
560
-280
35
Which of the following are like radicals? Check all of the boxes that apply.
\
The like radicals are 3x√x²y, –12x√x²y, x√yx² and 2√x²y.
What are radicals?A radical expression is an expression containing a square root.
Given are some expressions,
Like radicals are those whose entities in the square root are the same.
So, from the given options, like radicals are:
3x√x²y = This is like radical with the entity x²y inside the square root.
–12x√x²y = This is like radical with the entity x²y inside the square root.
x√yx² = This is like radical with the entity x²y inside the square root.
2√x²y = This is like radical with the entity x²y inside the square root.
Hence, The like radicals are 3x√x²y, –12x√x²y, x√yx² and 2√x²y.
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Peyton is a teacher and takes home 87 papers to grade over the weekend. She can grade at a rate of 7 papers per hour. How many papers would Peyton have remaining to grade after working for 12 hours
Answer:
Peyton would have 3 papers remaining to grade after working for 12 hours.
Step-by-step explanation:
1. Make an equation to represent this problem.
87 - (7 * 12) = r
(r represents how many papers are remaining after 12 hours.)
2. Solve 7 * 12.
87 - (84) = r
3. Subtract.
3 = r
5. Write the following Arithmetic Sequence using an Explicit Formula: a₁ = 8, an = an-1-2
an = 8+2(n-1)
an=8-2(n-1)
an=2-8(n-1)
an=2+8(n-1)
The explicit formula of the sequence is (b) a(n) = 8 - 2(n - 1)
How to determine the explicit formulaFrom the question, we have the following parameters that can be used in our computation:
a₁ = 8,
aₙ = aₙ₋₁ - 2
In the above sequence, we can see that the 2 is subtracted from the previous term to get the current term
This means that
first term, a = 8
common difference, d = -2
The nth term is then represented as
a(n) = a + (n - 1)d
Substitute the known values in the above equation, so, we have the following representation
a(n) = 8 + (n - 1) * -2
Evaluate
a(n) = 8 - 2(n - 1)
Hence, the explicit is (b) a(n) = 8 - 2(n - 1)
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Increase by
50%
Decrease by
5%
A number went into this machine and 57 came out.
What number went in?
Answer:
Step-by-step explanation:
Let x be the number that went in,
[x(1+50%)]x(1-5%)=57
x(1+50%)=60
x=40
The solution is, the number went in is 40.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
given that,
when a number Increase by 50% & Decrease by 5%,
then, A number went into this machine and 57 came out.
Let x be the number that went in,
so, using the given condition, we get,
[x(1+50%)]x(1-5%)=57
x(1+50%)=60
x=40
Hence, The solution is, the number went in is 40.
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a tea shop sells 42 varieties of boxes of tea. iroh purchases 5 boxes of tea. how many ways are there for iroh to make a selection if there is no restriction on the varieties of tea purchased from the shop?
The following account and correponding balance were drawn from Dexter Company’ Year 2 and Year 1 year-end balance heet. Account Title Year 2 Year 1
Bond payable $213,600 $302,000
Common tock 374,900 282,100
Other information drawn from the accounting record:
Dividend paid during the period amounted to $38,400. There were no bond liabilitie iued during the period. Required
a. Compute the amount of cah flow aociated with the repayment of bond liabilitie. B. Compute the amount of cah flow aociated with the iue of common tock. C. Prepare the financing activitie ection of the tatement of cah flow
the dividend payment from the proceeds from the issuance of common stock to get our total financing activities of $54,400.
A. Cash flow associated with repayment of bond liabilities: $88,400
B. Cash flow associated with the issuance of common stock: $92,800
C. Financing activities section of the statement of cash flow:
Bonds payable:
Repayment of bonds payable ($88,400)
Common stock:
Proceeds from issuance of common stock 92,800
Dividends paid (38,400)
Total financing activities $54,400
The financing activities section of the statement of cash flow shows the cash flow associated with all financing activities of the company. First, we calculate the cash flow associated with the repayment of the bonds. We subtract the Year 2 balance from the Year 1 balance, which gives us a cash flow of $88,400. Next, we calculate the cash flow associated with the issuance of common stock. We subtract the Year 1 balance from the Year 2 balance, which gives us a cash flow of $92,800. Finally, we subtract
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Factor the perfect-square trinomial in y = (x2 2x 1) − 1− 1. y = (x )2 − 1 −1
The perfect square trinomial in y = ( [tex]x^{2} + 2x + 1[/tex] ) -1 - 1 will be
⇒ [tex](x+1)^{2}[/tex]
The perfect square trinomial in y = (x + 2)2 - 1 - 1 will be
⇒ Null
A perfect square trinomial can be expressed as the square of a binomial,
We can write the first expression as,
y = [tex]x^{2} + 2x + 1[/tex]
y = [tex]x^{2} + 2x + 1 - 2[/tex]
⇒ [tex]x^{2} + x + x + 1[/tex]
⇒ [tex]x(x + 1) + 1(x + 1)[/tex]
⇒ (x + 1) (x + 1)
⇒ [tex](x + 1)^{2}[/tex]
Therefore, according to the first expression, [tex](x^{2} + 2x + 1) -1 - 1[/tex] is a perfect square binomial with the factor = [tex](x + 1)^{2}[/tex]
According to the second expression, y = (x +2)2 − 1 −1
This expression does not show any factors
Therefore, this second expression doesn't have any perfect square trinomial factors.
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Factor the perfect-square trinomial in y = (x2 + 2x + 1) − 1− 1, y = (x +2)2 − 1 −1
Answer: 1
Step-by-step explanation:
got it right
Which theorem shows that △ABC ≅ △DEF?There
are two triangles, triangle ABC and triangle DEF. Side AB is congruent
to side DE, side AC is congruent to side DF, side BC is congruent to
side EF.
A. The triangles are not congruent.
B. SAS Triangle Congruence Theorem
C. Isosceles Triangle Theorem
D. SSS Triangle Congruence Theorem
Answer:
D
Step-by-step explanation:
The correct answer is D. The SSS Triangle Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In the given situation, triangle ABC and triangle DEF are congruent because all three sides of triangle ABC are congruent to the corresponding sides of triangle DEF.
The drama club i elling ticket to their play to raie money for the how' expene. Each tudent ticket ell for $5 and each adult ticket ell for $7. 50. The auditorium can hold at mot 125 people. The drama club mut make no le than $790 from ticket ale to cover the how' cot. If 73 adult ticket were old, determine all poible value for the number of tudent ticket that the drama club mut ell in order to meet the how' expene. Your anwer hould be a comma eparated lit of value. If there are no poible olution, ubmit an empty anwer
This means that in order to make at least $790, the drama club must sell 47 number of student tickets. 47,48,49,50,51
The first equation is 5x + 7(73) = 790, where x is the number of student tickets. We can solve this equation to determine that x = 47. This means that in order to make at least $790, the drama club must sell 47 student tickets. Then, we can check the other possible values of x to see how many tickets they must sell. The other possible values are 48, 49, 50, and 51. Therefore, the answer is 47, 48, 49, 50, 51.
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Which expression finds enzo’s net worth? 127,100 dollars minus 88,500 dollars 127,100 dollars divided by 88,500 dollars 88,500 dollars 127,100 dollars 88,500 dollars minus 127,100 dollars
An expression that finds Enzo's net worth is:
$ 127100 - $ 88500.
What is the net worth?
The amount by which the value of the assets exceeds the liabilities is the net worth (equity) of the business. The net worth reflects the amount of ownership of the business by the owners. The formula for computing net worth is. Assets - Liabilities = Net Worth.
Enzo's net worth is the difference between the amount of money he has and the amount of money he owes. Therefore, the correct expression is: 88,500 dollars minus 127,100 dollars.
net worth = Assets - liabilities
net worth = 127100 - 88500
net worth = 38600.
This expression would give us the difference between the two amounts, which is the net worth.
The other expressions are not correct because they do not represent the difference between the two amounts.
127,100 dollars minus 88,500 dollars would give us the difference between the two amounts, but this difference would be the opposite of the net worth.
127,100 dollars divided by 88,500 dollars would give us the ratio of the two amounts, which is not the same as the net worth.
88,500 dollars is just the amount of money that Enzo has, and it does not take into account the amount of money he owes.
127,100 dollars is just the amount of money that Enzo owes, and it does not take into account the amount of money he has.
Hence, An expression that finds Enzo's net worth is:
$ 127100 - $ 88500
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find a recurrence relation for the number of bit sequences of length n with an even number of 0s.
The recurrence relation for the number of bit sequences of length n with an even number of 0s is 2 [tex]a_{n-1}[/tex] for n>=2 and a1=1.
Let a be the even number of 0s in all the bit sequences of length n.
1st instance. The sequence begins with a 1, and there are [tex]a_{n-1}[/tex] such strings of length n-1 that must contain an even number of 0s.
Second instance. The sequence must begin with a 0, followed by an odd number of 0s in the subsequent n-1-length sequence. An even number of 0s can be found in one of the [tex]2^{n-1}[/tex] possible bit strings, so [tex]2^{n-1} -a_{n}[/tex] strings have an odd number of 0s.
[tex]a_{n}= a_{n-1}+2^{n-1} -a_{n-1}\\a_{n}=2^{n-1}[/tex]
Therefore, the recurrence relation is
an = 2[tex]a_{n-1}[/tex] for n >= 2.
a1 = 1.
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Find the equation of the quadratic given its real roots 2-√3 and 2+√3 which passes through the point (1, -2).
Step-by-step explanation:
the factors are x-2+sqrt(3) and x-2- sqrt(3)
the basic form of the quadratic is x^2-4x+1, multiplying those factors together (there are 9 terms)
y=a(x^2-4x+1) is the general form
-2=a(-2)
a=1
a=(2/11)
the equation is y=x^2-4x+1
The punnett square shows the results when two parent dogs are crossed. L represents the allele for a long tail, and l represents the allele for a short tail. Which best describes this inheritance pattern? incomplete dominance because neither allele for tail length is dominant codominance because neither allele for tail length is dominant incomplete dominance because the offspring display an intermediate form of tail length codominance because the offspring display an intermediate form of tail length.
The best description for the inheritance pattern will be incomplete dominance because the offspring display an intermediate form of tail length.
The relationship is referred to be "complete dominance" when the phenotype (the observable trait) of the heterozygote is identical to the dominant homozygote. Complete dominance isn't necessarily the result, but rather imperfect supremacy, as heredity is full of variances and changes.
Although we are aware of total dominance, you might still be unclear as to how partial dominance varies. Is it essentially what the name implies? When one allele for a certain trait is not completely dominant over its counterpart, this is known as partial dominance (or the other allele). The outcome is a mixed phenotype, which is evident in the progeny.
Why does this matter? Each parent's characteristics are neither dominant nor recessive. A third phenotype that combines the traits of the two homozygotes results from a partial dominance relationship between two alleles; this is known as a "intermediate form of inheritance." The features are combined and appear to be "blended," but the alleles do not blend yet, partial dominance is frequently referred to as "blending."
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Answer: incomplete dominance because the offspring display an intermediate form of tail length.
Or C.
Step-by-step explanation:
taking the test on edge
HELP! I HAVE ONLY 40 mins left!!!! 53 POINTS AND BRIANLYEST
Select the graph for the solution of the open sentence. Click until the correct graph appears.
|x| + 1 > 7/2
Answer:
graph C
Step-by-step explanation:
if x≥ 0
x + 1 > 7/2
x > 7/2 - 1
x > (7-2)/2
x > 5/2
if x < 0
-x + 1 > 7/2
- x > 7/2 - 1
- x > 5/2
x < -5/2
final solutions
x < -5/2 ∨ x > 5/2
pooja's plant began sprouting 222 days before pooja bought it, and she had it for 989898 days until it died. at its tallest, the plant was 303030 centimeters tall. h(t)h(t)h, (, t, )models the height of pooja's plant (in centimeters), ttt days after she bought it. which number type is more appropriate for the domain of hhh?
If Pooja's plant began sprouting 2 days before Pooja bought it, and she had it for 98 days until it died , then the most appropriate for the domain of h is (c) -2 ≤ t ≤ 98 .
The term Domain is defined as the set of its possible inputs .
number of days before which the Pooja's plant sprouted = 2 days ,
the number of days Pooja had the plant is = 98 days ,
the height of the plant is denoted by the function ; h(t) .
where "t" is the number of days after she bought the plant .
From the above data , we can conclude that the domain for the function h(t) is -2 ≤ t ≤ 98 .
Therefore , the correct option is (c) -2 ≤ t ≤ 98 .
The given question is incomplete , the complete question is
Pooja's plant began sprouting 2 days before Pooja bought it, and she had it for 98 days until it died. at its tallest, the plant was 30 centimeters tall. h(t) models the height of Pooja's plant (in centimeters), t days after she bought it. Which number type is more appropriate for the domain of h ?
(a) 0 ≤ t ≤ 30
(b) 0 ≤ t ≤ 100
(c) -2 ≤ t ≤ 98
(d) 2 ≤ t ≤ 30
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imagine that we rolled a fair, six-sided die 1,000 times. out of 1,000 rolls, how many times do you think the die would come up even (2, 4, or 6)?
Probability of Number of outcome is an even in likely situation is given as 512
Given that;
Number of time die roll = 1,000
Find:
Probability of Number of outcome is an even
Computation:
Probability of an even = 3 / 6
Probability of an even = 1 / 2
Probability of Number of outcome is an even = [Probability of an even]1000
Probability of Number of outcome is an even = [1/2]1000
Probability of Number of outcome is an even = 500
So most likely outcome is 512
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slope: 3; y-intercept: -8
Answer:
Use desmos to help with slopes and finished equations its a graphing calculator and its very helpful
Step-by-step explanation:
Answer:
y=3x-8
Step-by-step explanation:
slope, or m (3), is always next to an x. y-intercept (-8) goes always after the mx
If 1=3
2=3
3=5
4=4
5=4
Then, 6=?
If 1=3, 2=3, 3=5, 4=4, and 5=4, then it is not possible to determine the value of 6. In this scenario, the numbers are not being used in a consistent or logical manner, so it is impossible to predict what value 6 might have. In general, it is not possible to determine the value of a number based on a series of equations that do not follow the rules of arithmetic.