Answers
Step-by-step explanation:
any linear function represents a straight line (hence the name) and is therefore of the structure
y = f(x) = ax + b
"a" is the slope of the line, and it is represented by the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another point.
"b" is the y-intercept (the y-value when x = 0).
so, let's look at the answer options :
A.
x = 0 gives us b (the y value) : 2
so, then for x = 1, y = 3 ?
3 = a×1 + 2
a = 1
now, the next point must be also on the same line for the whole function to be linear (and that means the equation has to be true for all numbers involved) :
x = 2, y = 6
6 = 1×2 + 2 = 4
6 is for sure NOT 4, so this is not a linear function.
it is actually y = x² + 2
B.
x = 0 gives us b : 1
for x = 1, y = 3 ?
3 = a×1 + 1
a = 2
again, the next point must be on the same line :
x = 2, y = 9
9 = 2×2 + 1 = 5
9 is for sure NOT 5, so this is not a linear function.
it is actuality y = 3^x.
C.
x = 0 gives us b : 0
for x = 1, y = 1 ?
1 = a×1 + 0 = a
a = 1
the next point :
x = 2, y = 4
4 = 1×2 = 2
4 is for sure NOT 2, so this is not a linear function.
it is actually y = x².
D.
x = 0 gives us b : 3
for x = 1, y = 9
9 = a×1 + 3
a = 6
the next point(s) must fit :
x = 2, y = 15
15 = 6×2 + 3 = 12 + 3 = 15
correct
x = 3, y = 21
21 = 6×3 + 3 = 18 + 3 = 21
correct
yes, this is a linear function.
it is y = 6x + 3
Related Questions
Use four rectangles to estimate the area between the graph of the function f(x) = V3x + 5 and the x-axis on the interval[0, 4] using the left endpoints of the subintervals as the sample points. Round any intermediate calculations, if needed, to noless than six decimal places, and round your final answer to three decimal places.
Answers
Answer:
12.123
Step-by-step explanation:
You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.
Riemann sumWhen the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.
The area we want is the sum ...
f(0) +f(1) +f(2) +f(3)
As the attachment shows, that sum is ...
area ≈ 12.123 . . . square units
__
Additional comment
The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.
Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.
For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.
Find a polynomial function of degree 4 with - 1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
The polynomial function in expanded form is f(x) = _
(Use 1 for the leading coefficient.)
Answers
Answer: [tex]f(x)=x^4 +3x^3 +3x^2 +x[/tex]
Step-by-step explanation:
[tex]f(x)=x(x+1)^3 \\\\=x(x^3 +3x^2 +3x+1)\\\\=x^4 +3x^3 +3x^2 +x[/tex]
Solve this inequality
Answers
[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-8\leq 10-2x < 28 } \end{gathered}$} }[/tex]
Separate the inequality compound in the inequality system.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{{\left\{ \begin{array}{r}10-2x\geq -8 \\ 10-2x < 28 \ \end{array} \right.} } \end{gathered}$} }[/tex]
We solve to: 10 - 2x < 28Order the unknown terms to the left side of the equation.[tex]\boxed{\bf{-2x < 28-10 }}[/tex]
Calculate the sum or difference.
[tex]\boxed{\bf{-2x < 18 }}[/tex]
Divide both sides of the equation by the coefficient of the invariable.[tex]\boxed{\bf{x > -\frac{18}{2} }}[/tex]
Clear the common factor
[tex]\boxed{\bf{x > -9} }}[/tex]
We solve to: 10 - 2x ≥ -8Order the unknown terms to the left side of the equation.
[tex]\boxed{\bf{-2x\geq -8-10 }}[/tex]
Calculate the sum or difference.
[tex]\boxed{\bf{-2x\geq -18 }}[/tex]
Divide both sides of the equation by the coefficient of the invariable.
[tex]\boxed{\bf{x\leq \frac{-18}{-2} }}[/tex]
Determine the sign of multiplication and division.
[tex]\boxed{\bf{x\leq \frac{18}{2} }}[/tex]
Clear the common factor
[tex]\boxed{\bf{x\leq 9}}[/tex]
[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{x > -9 \ and \ x\leq 9 } \end{gathered}$} }[/tex]
We find the intersection.
Answer = [tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-9 < x\leq 9 } \end{gathered}$} }[/tex]
Alternative forms: x ∈ (-9, 9]I need help with Systems of 2 equations Word Problems. Could some one help?
Answers
Let x be the number of children and let y be the number of adults.
We know that the total number of attendants was 147, then:
[tex]x+y=147[/tex]We also know that each child ticket cost $4 and for each adult cost $12, and the total amount collected were $1156. Then we have:
[tex]4x+12y=1156[/tex]Hence we have the system:
[tex]\begin{gathered} x+y=147 \\ 4x+12y=1156 \end{gathered}[/tex]Now we have to solve the system. To do that we solve the first equation for y:
[tex]y=147-x[/tex]and we plug this value into the second equation and solve for x:
[tex]\begin{gathered} 4x+12(147-x)=1156 \\ 4x+1764-12x=1156 \\ -8x=1156-1764 \\ -8x=-608 \\ x=\frac{-608}{-8} \\ x=76 \end{gathered}[/tex]Now that we have the value we can find the value of y, then:
[tex]\begin{gathered} y=147-76 \\ y=71 \end{gathered}[/tex]Therefore there were 76 children and 71 adults.
What does the leading term of −5x^4+4x^3−6x^2+8 tell you?
Answers
Step-by-step explanation:
The leading term is -5x^4, which tells us the highest degree of the polynomial.
The leading term in the equation tells us about the degree and whether the curve opens outwards on inwards
What is an equation in one variable?
An equation is a polynomial in one variable with a finite degree
We are given an equation
[tex]-5x^4+4x^3-6x^2+8[/tex]
In this the leading term is -5x^4
Here the coefficient is negative this tells us that the curve opens downwards. if the coefficient has been positive then the curve would open outwards.
Also from the leading term we can find out the degree of the highest variable. the degree of highest variable in this case is 4
Hence, The leading term in the equation tells us about the degree of the variable and whether the curve opens outwards on inwards
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Could you provide a step by step resolution for this question?
Answers
Given:
Angle A = 120 degrees
Side opposite angle C = 150 meters
Side opposite angle B = 275 meters
Find:
Angle B
Solution:
Since we have two sides given and an included angle, we can use cosine law.
Let's look for the length of the side opposite Angle A first.
[tex]a^2=b^2+c^2-2bc\cos A[/tex]where a = length of the side opposite Angle A or side BC
b = side opposite Angle B or Side AC
c = side opposite Angle C or Side AB
A = Angle A
Since we already have the data above, let's plug it in to the formula we have.
[tex]a^2=275^2+150^2-2(275)(150)\cos 120[/tex]Then, solve a.
[tex]\begin{gathered} a^2=75,625+22,500-82,500(-0.5) \\ a^2=98,125+41,250 \\ a^2=139,375 \\ \sqrt[]{a^2}=\sqrt[]{139,375} \\ a\approx373.3296\approx373.33 \end{gathered}[/tex]Hence, the length of side opposite a or Side BC is approximately 373.33 meters.
Now, to solve for Angle B, we can use the sine law.
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]Let's plug in the value of Angle A, side BC or a, and side AC or b to the formula.
[tex]\frac{\sin120}{373.3296}=\frac{\sin B}{275}[/tex]Then, solve for Angle B.
[tex]\begin{gathered} \sin B=\frac{275\sin 120}{373.3296} \\ \sin B=0.6379268552 \\ B=\sin ^{-1}0.6379268552 \\ B\approx39.64 \end{gathered}[/tex]Therefore, the bearing of ship C from ship B is approximately 40 degrees. (rounded off to the nearest degree)
Triangle HIJ is similar to triangle KLM. Find the measure of side LM. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.
Answers
Given the following question:
We know the two triangles are similar
We also have the bases of the two triangles which means we can find how bigger the second triangle is, compared to the first triangle.
[tex]\begin{gathered} 5\times3.6=18 \\ 7\times3.6=25.2 \\ 25.2\text{ is already rounded to the nearest tenth} \\ LM=25.2 \end{gathered}[/tex]Which value makes the equation 5b + 15 = 30 true?
A b=3
B b=9
C b= 10
D b=75
Answers
Answer:
Hello! The answer is A) B=3
Step-by-step explanation:
Hope I helped! Please mark brainiest if get chance.
(Ps: Are you an army?)
Then subtract 15 on both sides
5b=15
Divide 5 by 15
B=3
So , (5 x 3)+ 15= 30, would make this equation true.
I hope this helps :)
Write the correct expression for the following statement:
x six times
Answers
x^6
Step-by-step explanation:
I don't know how to explain but I think this is what you mean
4. Which number produces anirrational answer when multipliedby 0.79?A.B. 0.383838...C. 0.12D.קשותU
Answers
Recall that the product between two rational numbers is always a rational number, and the product between an irrational number and a rational number different from zero is always an irrational number.
Also, recall that a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.
Now, notice that:
[tex]\begin{gathered} 0.79=\frac{79}{100}, \\ 0.383838\ldots=\frac{38}{99}, \\ 0.12=\frac{12}{100}. \end{gathered}[/tex]Therefore, 0.79, 0.383838..., 0.12 are rational numbers.
Now, recall that:
[tex]\sqrt[]{7}[/tex]is an irrational number.
Therefore, the product between 0.79 and √7 is an irrational number.
Answer: Option A.
The quotient of 134 and z is the same as 374
Answers
We will ahve the following:
[tex]\frac{134}{z}=374[/tex]B= (s+z/2) m solve for s
please help i need to get my grade up
Answers
Answer:
See below
Step-by-step explanation:
1. Multiply m to get, m(s + z)/2 => (ms + mz)/2
2. Mutiply by 2 by both sides
2B = MS + MZ
3. Divide By M
2B = M(S+Z)
2B/M = S+Z
4. Minus Z
(2B/M - Z) = S
Isaac wants to play miniature golf. Go Golf charges $2.50 for ball and club rental and $4.25 per game. Golf Games charges $3.25 for ball and club rental and $8.50 for two games. For how many games would the cost be the same? Write and solve an equation to determine the number of games for which the cost would be the same.
NEED FAST RESPONSE EQUATION AND SOLUTION
Answers
The equation is 6.75x = 5.875y
The price will be the same for 47 Go Golf games and 54 Golf Games
Go Golf charges for the ball and club rental = $2.50
Go Golf charges per game = $4.25
Total charges for Go Golf for one game = $6.75
Golf Games charges for the ball and club rental = $3.25
Golf Games charges for two games = $8.50
Total charges for Golf Game for two games = $11.75
Per game charges = $11.75/2 = $5.875
Let x be the number of games for Go Golf and y be the number of games for Golf Games
Formulating the equation we get:
6.75x = 5.875y
Converting into fractions we get:
675/100x = 5875/1000y
27/4x = 47/8y
After cross multiplication
x/y = 57/48
x = 57 and y = 48
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which of the following equations would not contain the point (4,12)?
A. y=1/2x+8 B. y= -2x+20
Answers
Answer:
A is the answer :))))))))))))))))))
find 10-3. write the subtraction fact tow ways?
Answers
Answer:
10 - 3 = 7
10 - 7 = 3
Step-by-step explanation:
How many 1/4 pound hamburgers could be made from 5 1/2 pounds of hamburger meat?
Answers
Given:
Total amount of hamburger meat = 5½ pounds
Let's find how many ¼ pound hamburgers could be made from 5½ pounds of hamburger meat.
To find how many pound hamburger could be made divide 5½ by ¼.
Thus, we have:
[tex]5\frac{1}{2}\div\frac{1}{4}[/tex]To perform the division, take the following steps:
Step 1:
Convert the mixed fraction to improper fraction
[tex]\frac{11}{2}\div\frac{1}{4}[/tex]Step 2:
Flip the fraction on the right and change the division symbol to multiplication
[tex]\begin{gathered} \frac{11}{2}\ast\frac{4}{1} \\ \\ =\frac{11\ast4}{2\ast1} \\ \\ =\frac{44}{2} \\ \\ =22 \end{gathered}[/tex]Therefore, 22 of ¼ pound of hamburger could be made from 5½ pounds of hamburger meat.
ANSWER:
22
Determine whether the distribution represents a discrete probability distribution. Justify your answer
Answers
The probability distribution is given in the table.
The condition for the probability distribution is
1. The sum of the probability distribution is 1.
2. The probabilities value range between 0 and 1.
Condition to check the probability distribution
[tex]0.35+0.25+0.22+0.12=0.94[/tex]The sum of the probability is not equal to 1.
Hence the distribution does not represents a discrete probability distribution.
how do i graph the equation y=2000x+4000
Answers
Answer:
first draw the line edges and vertical
second put the dot every no.
And put the y=2000×+4000
An investment firm invested in two companies last year. They invested $12,000 in Company A and made a profit of 14%. They
invested $8000 in Company B and made a profit of 21%.
Answer the questions below. Do not do any rounding.
(a) What was the investment firm's total profit?
$0
(b) What was the percent profit for their total investment?
Answers
The investment firm's total profit is $ 3360 and the percent profit for their total investment is 16.8%.
How to calculate percentage of a situation?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it. There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.
Formula for percentages: (Value/Total value) * 100
Given, amount invested in company A = $ 12,000
Amount invested in company B = $ 8000
Profit earned by company A = 14%
Profit earned by company B = 21%
Amount in profit earned from company A = (12000*14)/100 = $ 1680
Amount in profit earned from company B = (8000*21)/100 = $ 1680
Therefore total profit of the investment firm = $ (1680 + 1680) = $ 3360
Thus, the investment firm's total profit is $ 3360.
Now, percentage profit of total investment = (3360/20000)*100 = 16.8%, using available literature and formula.
Thus, the percent profit for their total investment is 16.8%
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Using SSS, SAS, ASA, & AAS WITH CONGRUENT TRIANGLES For each problem below, state each of the following: a ) state the congruent parts b )state how the triangles are congruent c ) state the congruence
Answers
Given two triangles, ADB and CBD
So,
1. the measure of < D = the measure of angle < B
2. CB = AD
3. BD = DB
so, the triangle ADB is congruent to the triangle CBD by SAS [ side - angle - side ]
So, the corresponding parts are congruent :
So,
1. the measure of angle A = the measure of angle C
2. the measure of angle B = the measure of angle D
3. AB = CD
If 8 - x = 17, then find the value
of 6x - 22
Answers
Answer: -25
Step-by-step explanation: 8 - x = 17 ~ x=-9 6*(-9)-22=-25
hello i have a upcoming test and want to know how to solve this
Answers
Expression given:
[tex]g>1[/tex]To know how to graph the given expression, it is easier if we determine what it means in words. In this case, this expression means all the values above one (without including one).
We know that one is not included as it has the sing ">", if the value were included, then it would have the sing "≥" or "≤".
This is important because when you are graphing, a discontinuous line is drawn for values not included, and a continuous one for included values.
Now, we would have to evaluate if it is the independent variable (generally called x), or the dependent variable (generally called y).
Assuming that g is the dependent variable, then the graph would be like this:
However, if the variable was de independent variable, then it would look like this:
We have to note that both graphs go from 1 to bigger values.
A cube has a surface area of 253 square inches.What is the area of one face of the cube in sqaure inches.
Answers
Answer:
42 1/6 square inches
Step-by-step explanation:
253=6x
x=42 1/6
42 1/6 square inches
:]
Name the transformations happening to the absolute value parent function, f(x) = |x|, in each of the following in the correct order.
Answers
is one
the Answer:
Step-by-step explanation:
1
what is the base and coefficient of the exponential function:
Answers
Given an exponential function
[tex]\begin{gathered} y=ab^x \\ \text{ wh}ere\text{ a and b are constants} \\ \text{then a is the coefficient} \\ \text{and b is the base} \end{gathered}[/tex]Therefore,
10 is the coefficient and 1/5 is the base
n
4 Which expression is equivalent to 8.508 ÷ 70.9?
A 8.508 709
B 85.08 709
C 850.8 709
D 8,508 709
5 What is the value of 0.5 ÷ 0.8? Show your work.
Answers
Answer:
a because 8.508
Step-by-step explanation:
0.625 so it easy 0.5:0.8
What does the fundamental theorem of algebra state about the equation 2x2−x+2 = 0?Question 5 options:The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots arex = 1±i15√4.The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1±i15√4.
Answers
Given
Equation
[tex]2x^2-x+2=0[/tex]Procedure
The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are
[tex]x=\frac{1}{4}\pm\frac{\sqrt[]{15}}{4}[/tex]The discriminant b^2 - 4ac < 0
so, there are two complex roots.
Assume that AGHI ALMN. Which of the following congruence statements
are correct? Check all that apply.
A. ZN=21
B. ZL 41
C. ME ZH
☐ D. GH = LM
E. IG= LM
F. IH NM
Answers
The following congruence statements a, b, e, f are correct.
What is congruence in a triangle?
Triangle congruence: If all three corresponding sides and all three corresponding angles seem to be equal in size, two triangles are said to be congruent.
When two triangles are congruent, their sides and corresponding angles are identical.
Therefore, if GHI is congruent to LMN, then GH =LM, HI=MN and GI=LN, and also angle G=angle L, Angle H=angle M, while angle I = angle N, therefore the correct answers is f) ∠M= ∠H, (a) GH = LM b) ∠L=∠G. and e)IH=NM.
Therefore, option a, b, e, f are correct.
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If L, M and N are the midpoints of the sides of the triangle PQR, PR= 46, PQ = 40, and LN = 17, find each measure.; LM, MN, QR and the perimeter of LMN
Answers
LM = 23; MN = 20 ; QR = 34 ; Perimeter of LMN is 60
Here, we want to find the measures
From what we have, triangle LMN is formed by joining the midpoints of the triangle PQR
From the midpoint theorem, the sides of PQR are parallel and exactly half the measure of the sides they face
For example, LM is half PR
a) LM
[tex]LM\text{ = }\frac{1}{2}\times PR\text{ = }\frac{1}{2}\times46\text{ = 23}[/tex]b) MN
[tex]MN\text{ = }\frac{1}{2}\times PQ\text{ = }\frac{1}{2}\times\text{ 40 = 20}[/tex]c) QR
Here, QR will be twice the measure of LN
[tex]QR\text{ = 2}\times LN\text{ = 2}\times17\text{ = 34}[/tex]d) To find the perimeter of LMN, we have to add up the measure of the side lengths
We have this as;
[tex]\text{LMN = LM + LN + MN = 23 + 17 + 20 = 60}[/tex]For the function f(x), = 10 (√x + 9), find f-¹(x).
Answers
The inverse of the function f(x) = 10 (√x + 9) is f⁻¹(x) = (x - 90)² / 100
Given,
The function, f(x) = 10 (√x + 9)
We have to find the inverse of the function, f⁻¹(x)
Here,
f(x) = 10 (√x + 9)
f(x) = 10√x + 90
Replace f(x) with y.
y = 10√x + 90
Swap x with y;
x = 10√y + 90
Solve for y
That is,
x = 10√y + 90
x - 90 = 10√y
(x - 90) / 10 = √y
Square both sides
((x - 90) / 10)² = √y²
(x - 90)² / 100 = y
Replace y with f⁻¹(x)
That is,
f⁻¹(x) = (x - 90)² / 100
Therefore,
The inverse for the function f(x) = 10 (√x + 9) is f⁻¹(x) = (x - 90)² / 100
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