The most appropriate choice for simultaneous linear equation will be given by -
Cost of one notebook is $1.70 and cost of one pen is $0.50
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
Let the cost of one notebook be $x and the cost of one pen be $y
John spent $10.50 on 5 notebooks and 4 pens.
So,
5x + 4y = 10.50 ........... (1)
Ariana spent $7.80 on 4 notebooks and 2 pens
So,
4x + 2y = 7.80 ............ (2)
Multiplying equation (2) by 2,
8x + 4y = 15.60 ............ (3)
Subtracting (1) from (3),
3x = 5.10
[tex]x = \frac{5.10}{3}[/tex]
[tex]x =[/tex] $[tex]1.70[/tex]
Putting the value of x in (1)
[tex]5 \times 1.70 + 4y = 10.50\\8,50 +4y = 4y = 10.50\\4y = 10.50 - 8.50\\4y = 2\\y = \frac{2}{4}[/tex]
y = $[tex]0.50[/tex]
Cost of one notebook is $1.70 and cost of one pen is $0.50
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Function f is a continuous linear function. Over which interval of the domain is function f positive?
X
-3
0
3
6
9
12
f (x)
4
3
0
-2
-4
-6
(-∞, 3)
(-∞, 0)
(0, ∞)
(-∞, ∞)
The function f is positive on the domain (-∞, 3)
The f(x) values corresponding to x-values are given. Also f(x) is a continuous linear function.
If we analyze the function values, the first 3 entries are positive, then from there the function values becomes negative.
Also it is clear from the function values that the function is decreasing from positive values to negative values.
The corresponding x-values for the positive values of the function are x = -3, x = 0 and x = 3.
Since f(x) is continuous linear function, the given x-values and f(x) values are not the only ones there. The domain and images are actually in the form of intervals, but here only certain values are given in the table.
Therefore, the function must be positive for x < -3 too.
Hence the domain where the function is positive becomes (-∞, 3).
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The game of Scrabble has 100 tiles. The diagram shows the number of tiles for each letter and the letter's point value. One tile is drawn from Scrabble's 100 tiles. If one tile is drawn from the 100 tiles, find the odds in favor and the odds against selecting an E.
From the scrabble information given above, the odds in favor of selecting E is given as 0.073 while the odds against selecting an E is 13.667.
What are the odds in math?The odds are defined as the chance of the event occurring divided by the probability of the event not occurring. If the chance of an event happening is Y, the probability of it not happening is 1-Y.
Given:
Total number of tiles = 100
Number of E tiles = 12 [See attached image]
The odds in favor of selecting E =
= no of cases in favor of E / no of cases against E
= 12 / ( 100 - 12)
= 6 / 82
= 0.0731707317
[tex]\approx[/tex] 0.073
Given the above,
The odds against selecting E = 82/6
= 13.6666666667
[tex]\approx[/tex] 13.667
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what is the maximal domain on the function x^2+8/x^2+4x-5?
Answer:
{x ∈ R: x ≠ -5 and x ≠ 1}.
Step-by-step explanation:
x^2+8/x^2+4x-5
= x^2+8 / (x - 1)(x + 5)
The denominator is zero when x = 1 or x = -5
So:
Domain is:
{x ∈ R : x ≠ -5 and x ≠ 1}.
W
E
Find the slope of the line shown below
-2 -1
slope =
4
3
2
1
-1
-3
-4
-5+
ينا
1
2
a
Answer:
slope = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line
m = [tex]\frac{-1-(-2)}{2-0}[/tex] = [tex]\frac{-1+2}{2}[/tex] = [tex]\frac{1}{2}[/tex]
If 111 people attend a concert and tickets for adults cost $3.5 while tickets for children cost $2.25 and total receipts for the concert was $347.25, how many of each went to the concert?
adults
children
Using equation, the number of children and adult tickets sold are 33 and 78 respectively
How to find number of each tickets?111 people attend the concert and tickets for adults cost $3.5 while tickets for children cost $2.25 and total receipts for the concert was $347.25.
Therefore, the number of ticket sold for adult and children can be calculated as follows :
let
x = number of children ticket sold
y = number of adult tickets sold.
Therefore, the equation that represent the situation is as follows:
2.25x + 3.5y = 347.25
x + y = 111
multiply equation(ii) by 3.5
2.25x + 3.5y = 347.25
3.5x + 3.5y = 388.5
subtract equation(i) from equation(ii)
1.25x = 41.25
divide both sides by 1.25
x = 41.25 / 1.25
x = 33
Hence,
y = 111 - 33
y = 78
Therefore,
number of children ticket = 33
number of adult ticket = 78
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yall what is 2 divided by 4/9
Answer:
4.5
Step-by-step explanation:
2/1 x 9/4 = 18/4 = 4.5
Answer:
4.5 is your answer
Step-by-step explanation:
hope it helps
calculate the sum of the infinite series S ∞=5-3+9/5-…A.)not possible B.)31/8C.)25/8D.)21/8
Looking at the series, we have a geometric sequence, where the first term is a1 = 5 and the common ratio is q = -3/5.
(This ratio can be calculated by dividing one term by the term before)
To find the sum of an infinite geometric sequence, we can use the formula below:
[tex]S_{\infty}=\frac{a_1}{1-q}[/tex]Since a1 = 5 and q = -3/5, we have:
[tex]S_{\infty}=\frac{5}{1-(-\frac{3}{5})}=\frac{5}{1+\frac{3}{5}}=\frac{5}{\frac{8}{5}}=5\cdot\frac{5}{8}=\frac{25}{8}[/tex]Therefore the correct option is C.
When you first looked at the image, you saw that Dina has 24 tickets for carnival rides, and she wants to use all of them. Some rides have a height requirement, and some rides do not have a height requirement.
-Dina has 24 tickets and wants to use all of them. She plans to go on a ride most once.
-Rides with no height requirement cost 3 tickets.
-Rides with a height requirement cost 4 tickets.
Let's answer the question "How many rides can Dina go on using all of her tickets?"
1. Which statements are true about the variables involved in this situation and the values for each variable? Select all that apply.
A. The variables should represent the number of tickets spent on rides with no height requirement and the number of tickets spent on rides with a height requirement.
B. The variables should represent the cost in tickets for rides with no height requirement and the cost in ticket for rides with a height requirement.
C. The values for the variables can be any real number.
D. The values for the variables can be any nonnegative integers.
2.To answer the question, think about the strategy you would use along with all the information you have. What answer do you get? Select all that apply.
Note that 3-ticket rides have no height requirement, and 4-ticket rides have a height requirement.
A. 3-ticket rides: 0; 4-ticket rides: 6
B. 3-ticket rides: 2; 4-ticket rides: 6
C. 3-ticket rides: 4; 4-ticket rides: 3
D. 3-ticket rides: 6; 4-ticket rides: 2
E. 3-ticket rides: 8; 4-ticket rides: 0
3.D. Does your answer make sense in the context of the situation? How do you know? Select the correct words to complete the answer.
The answer makes sense in the context of the situation because the numbers of rides are A._______ and the number of tickets totals B._______.
1. The statements that are true about the variables involved in this situation and the values for each variable are:
A. The variables should represent the number of tickets spent on rides with no height requirement and the number of tickets spent on rides with a height requirement2. The number of rides Dina can go on using all of her tickets are
C. 3-ticket rides: 4; 4-ticket rides: 33. Yes, The number of rides equals the total number of tickets while maintaining going for a ride most once
The answer makes sense in the context of the situation because the numbers of rides are A. 7 and the number of tickets totals B. 24
How to find how many rides can Dina go on using all of her ticketsgiven data
Dina has 24 tickets for carnival rides
She plans to go on a ride most once
Rides with no height requirement cost 3 tickets
Rides with a height requirement cost 4 tickets
1. The given statement includes: She plans to go on a ride most once. This means that Dina will not have a zero ride.
zero is a real number and a non negative integer hence option A is correct
2. Option C maintains she plans to go on a ride most once and the number of tickets used totals 24
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If y is directly proportional to the square of x and x is 5 when y is10 what is the
constant of variation?
The constant of variation is 0.4.
What is constant of variation?
A direct variation's product of two variables or the product of two variables in an inverse variation The constant of variation is used in the direct variation equations = k and y = kx as well as the inverse variation equations xy = k and y = k.
We know that y is directly proportional to the square of x.
Therefore we can use the formula,
y = kx^2
Putting the values of x and y,
10 = k (5)^2
=> 10 = k .25
=> 10/25 = k
=> k = 0.4
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Solve for x.
8x = 4x-32
If the area to the right of x in a normal distribution is 0.543, what is the area to the left of x?
Answer:
.457
Step-by-step explanation:
The WHOLE area is = 1
so 1 - .543 = .457
Use degree and the sign of the leading
coefficient determine end behavior of the
corresponding graph. State the number of
possible x-intercepts and the value of the y-
intercept.
f(x)=x²+2x² - 4x²
2
As x approach to +∞ function y approaches -∞
And as x approach to -∞ function y approaches -∞
What is coordinate plane ?A coordinate plane is a two-dimensional surface created when two number lines are combined. When a horizontal line crosses the origin, which is the location where the X and Y axes meet, it is generated. A coordinate grid's integers are used to locate points. A coordinate plane can be used to graph points, lines, and a variety of other objects. It functions as a map and offers straightforward directions between two sites.
F(x)=[tex]x^{2} +2x^{2} -4x^{2}[/tex]
F(x)=-[tex]x^{2}[/tex]
if x =0 then y = 0
if x = 1 then y = -1
End behavior
As x approach to +∞ function y approaches -∞
And as x approach to -∞ function y approaches -∞
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Select the correct answer.
Which expression gives the same result as
4
Σ (5(1/3)i)?
i=0
The correct answer is [B]
Binary and unary operations are the two most popular forms of operations. Trigonometric functions and negation are examples of unary operations that use only one value. Contrarily, binary operations, which include addition, subtraction, multiplication, division, and exponentiation, only accept two values. Here the same expression will be 5 ∑([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex]
What is mathematical operation?Mathematical objects other than numbers can be used in operations. Logic operations like and, or, and not can be used to combine the logical values true and false. It is possible to add and subtract vectors. Utilizing the function composition operation, it is possible to combine rotations by first performing the first rotation and then the second. The binary operations union and intersection as well as the unary operation of complementation are operations on sets. Composition and convolution are two operations on functions.
Not all possible values of the domain may be covered by an operation's definition. For instance, it is impossible to square the roots of negative integers or divide by zero in real numbers. An operation's domain of definition, also known as the active domain, is the set of values for which the operation is specified. However, the set of real values obtained by the operation is its codomain of definition, active codomain, image, or range. The set that contains the values created is referred to as the codomain. [failed to verify] For instance, only non-negative numbers are produced by the squaring operation when applied to the real numbers; the set of real numbers is the codomain, but the non-negative numbers are the range.
4
∑(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex])
i=0
4
∑(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex])= (5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{0}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{1}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{2}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{3}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{4}[/tex])
0
= 5([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{0}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{1}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{2}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{3}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{4}[/tex])
4
= 5 ∑([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex])
i=0
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Find the value of x:
Answer: it should be 5
we can multiply 3x4 to get twelve so it must be the same for the other one
So 5x4=20
Step-by-step explanation:
have a great day!
Answer:
5
Step-by-step explanation:
12/4 = 3. 20/4 = 5
Side 12 divided by side 3 is four. You know four is now your key. Side 12 divided by 4 is Side 3. Side 20 divided by 4 is 5. So 5 is your answer.
Hope this helps! :)
7 * the smaller of two consecutive even integers is the same as -248 minus 6 * the larger integer. find the integers
7 * the smaller of two consecutive even integers is the same as -248 minus 6 * the larger integer. find the integers
let
x ----> the smaller of two consecutive even integers
x+2 -----> the second integer
so
7x=-248-6(x+2)
solve for x
7x=-248-6x-12
7x+6x=-248-12
13x=-260
x=-20
the second number is
-20+2=-18
the numbers are -20 and -181. An angle in a right triangle is identified as θ. If the tangent of θ equals one, what must be true about the triangle side lengths?
A. The side adjacent to theta is half the length of the hypotenuse.
B. The side opposite to theta is longer than the adjacent side.
C. The sides opposite and adjacent to theta are the same length.
D. The side adjacent to theta is longer than the adjacent side.
If the tangent of θ equals one (1), the true statement about the right-angled triangle side lengths is that: C. The sides opposite and adjacent to theta are the same length.
What is a tangent?In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.
Mathematically, the tangent of an angle is given by this expression:
Tanθ = Opp/Adj
Where:
Opp represents the opposite side of a right-angled triangle.Adj represents the adjacent of a right-angled triangle.θ is the angle.For this right-angled triangle, the tangent of the angle (θ) is given by:
Tanθ = Opp/Adj = 1
Opposite/Adjacent = 1
Cross-multiplying, we have:
Opposite = Adjacent
In conclusion, the opposite side length of this right-angled triangle is equal to its adjacent side length.
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Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.428. Find the probability that in a given year it will not snow on January 1st in that town.
The probability that in a given year it will not snow on January 1st in that town is 0.572.
How to calculate the probability?It should be noted that from the information, the meteorological records illustrates that the probability that it will snow in a certain town on January 1st is 0.428.
Therefore, the probability that in a given year it will not snow on January 1st in that town will be:
= 1 - 0.428
= 0.572
The probability is 0.572.
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The picture shows two sizes of shipping boxes with measurements in inches. The boxes are rectangular prisms.
There are two rectangular prisms. Prism 1 has a height of 10 inches, length of 20 inches and a width of 7 inches. Prism 2 is smaller and to the right of Prism 1. Prism 2 has a height of 4 inches, length is 20 inches and width is 4 inches.
Marcus shipped 1 of the larger boxes and 2 of the smaller boxes. Which equations show the total volume of the boxes Marcus shipped? Select the three equations that apply.
A.
(20×10×7) + [2× (20×4×4)]
B.
(20×10×7) × [2× (20×4×4)]
C.
(20×10×7) + (20×4×4) + (20×4×4)
D.
(20+10+7) + (20+4+4) + (20+4+4)
E.
(20×10×7) + [2+ (20×4×4)]
F.
(200×7) + [2× (80×4)] 3 /
The equations which show the total volume of the boxes Marcus shipped are as follows:
A. (20 × 10 × 7) + [2× (20 × 4 × 4)]
C. (20 × 10 × 7) + (20 × 4 × 4) + (20 × 4 × 4)
F. (200 × 7) + [2 × (80 × 4)]
How to calculate the volume of a rectangular prism?Mathematically, the volume of a rectangular prism can be calculated by using this equation:
Volume = L × W × H
Where:
L represents the length of a rectangular prism.H represents the height of a rectangular prism.W represents the width of a rectangular prism.For rectangular prism 1, the volume is given by:
Volume 1 = L × W × H
Volume 1 = 20 × 7 × 10
Volume 1 = 200 × 7
Volume 1 = 1,400 cubic inches.
For rectangular prism 2, the volume is given by:
Volume 2 = L × W × H
Volume 2 = 20 × 4 × 4
Volume 2 = 80 × 4
Volume 2 = 320 cubic inches.
Since Marcus shipped 1 of the larger boxes and 2 of the smaller boxes, the total volume of the boxes Marcus shipped is given by these three (3) equations:
(20 × 10 × 7) + [2× (20 × 4 × 4)](20 × 10 × 7) + (20 × 4 × 4) + (20 × 4 × 4)(200 × 7) + [2 × (80 × 4)]Read more on rectangular prism here: https://brainly.com/question/27130617
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The frequency (F) and length (L) of a wave are related by the following formula F x L = 3.0 x 10^10. Consider that wavelength of violet light is 1.3 x 10^-8. What is the frequency of violet light
Answer:
B: 2.3 x 10^18
expination:
Substitute values into the formula.
F x L = 3.0 x 10*10
F x 1.3 x 10^−8 = 3.0 x 10^10
F = 3.0 x 10^10 1.3 x 10^−8 F = 2.3 x 10^18
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Four times a number added to 7 times the number is 55. What is the number?
Answer:
12
Step-by-step explanation:
4xA+7=55
using PEMDAS multiplication comes first
A4+7=55
A4=55-7
A4=48
A=48/4
A=12
check:
4x12+7=12
Riley bought boxes of thank you cards and get well cards. The thank you cards came in boxes of 9 and the get well cards came in boxes of 4. Riley bought 5 boxes and got a total of 30 cards. How many boxes of each type of card did she buy?
Riley bought 2 boxes of thank you cards and 3 boxes of get well cards.
What is linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let Riley have bought x boxes of thank you cards and y boxes of get well cards.
Therefore according to the question,
x + y = 5.......(1)
9x + 4y = 30........(2)
Multiplying equation 1 with 4 we get.
4x + 4y = 20.......(a)
Subtracting (a) form (2) we get:
5x = 10
=> x = 2
Putting the value of in (1) we get y= 3
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Which table dose not show as a function x ?
Table b. doesn't show y as a function of x as is has to two x values for a same y value '100'.
What is a function?A function, as used in mathematics, is an expression that depicts the relationship between an independent variable (input) and a dependent variable (output), where only one output is possible for each input. In daily life and many professions, functions are useful.
For instance, assuming a constant stride length, a person's distance traveled in an hour is dependent on the number of steps taken. The same individual can extend their walking distance by merely changing the number of steps taken.
Similar to this, the quantity of goods sold may affect the amount of profit a bakery makes. The bakery will generate more revenue by offering more items. The function form of both of these examples is writable. In mathematics, function notation is used to express functions. Such as, f(x) = 3x+ 2
The meaning of y as a function of x is x is y is directly varied with x that is y = ax + b, so for every different x there is a unique y too,
But in Table b. there are two y whose values are 100 but the x are different
which is not possible.
Therefore, Table b. doesn't show y as a function of x as is has to two x values for a same y value '100'.
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which equation are correct select each other answers
Answer:
second and fourth are correct
Step-by-step explanation:
remembering the rule of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m +n)}[/tex]
then
- 7x²(4x³ + 2) = - 28[tex]x^{5}[/tex] - 14x² ≠ - 28[tex]x^{6}[/tex] - 14x²
- 2b³(6b² + 5) = - 12[tex]b^{5}[/tex] - 10b³ ← correct
- 3[tex]y^{4}[/tex] (5y² + 2) = - 15[tex]y^{6}[/tex] - 3[tex]y^{4}[/tex] ≠ - 15[tex]y^{8}[/tex] - 6[tex]y^{4}[/tex]
- 5d³ (3d² + 4) = - 15[tex]d^{5}[/tex] - 20d³ ← correct
I need help answering this question.
You have to determine which of the given square roots can be expressed as a fraction:
1) The square root of one is 1
[tex]\sqrt[]{1}=1[/tex]One can be expressed as a fracion:
[tex]1=\frac{1}{1}[/tex]So it is a rational number.
2) The square root of 2 is an irrational number and cannot be expressed as a fraction.
[tex]\sqrt[]{2}=1.414213562\ldots..[/tex]Its decimal expantion has no end, i.e. it has infinite decimal values.
3) Square root of three is an irrational number and cannot be expressed as a fraction.
[tex]\sqrt[]{3}=1.732050808\ldots.[/tex]4) The square root of 5 is an irrational number and cannot be expressed as a fraction.
[tex]\sqrt[]{5}=2.236067977\ldots..[/tex]In conclusion the only rational number in the given set is the square root of 1.
Find the z-value so that the area to the right of z (shaded in the picture) is 0.9429.
To determine the z-value so that the area to the right of z is 0.9429
[tex]\begin{gathered} Pr(0Hence the corresponding Z- score from the shaded picture of x - value 0.4429 = 1.58WORTH 35PTS
what is equivalent to (3^4)^6÷3^2
The required expression equivalent to the given expression is 3²² .
An expression in mathematics is said to be algebraic if it was constructed using integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
However, transcendental numbers like such and e are not algebraic because they are not created from integer constants and algebraic operations.While the definition of e necessitates an infinite number of algebraic operations, the generation of is frequently expressed as a geometric expression.If an expression can be reduced to a reasonable fraction using the features of arithmetic operations, it is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).Given : the expression of the form ( 3 ⁴ ) ⁶ ÷ 3²
Simplifying we get:
= ( 3 ⁴ ) ⁶ ÷ 3²
= 3⁽²⁴⁻²⁾
= 3²²
Therefore the required expression equivalent to the given expression is
3²² .
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I don’t really need a explanation just give answer
we know that
the coordinates of point A are (0,1) and point C(3,3)
Applying the formula to calculate the distance between two points
[tex]d=\sqrt{(3-1)^2+(3-0)^2}[/tex]therefore
The answer is option CHey can anyone pls answer this!
The graph of the linear function y = 2/3x + 1 is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, the function is given as follows:
y = 2/3x + 1.
From this, we have that:
The slope is of m = 2/3, hence when x changes by 1, y changes by 2/3, ..., when x changes by 3, y changes by 2, and so on.The intercept is of b = 1, meaning that the graph of the line crosses the y-axis at point (0,1).From the slope, when x changes by 3, y changes by 2, hence:
x -> x + 3: 0 -> 0 + 3, x = 3.y -> y + 2: 1 -> 1 + 2, y = 3.Thus the linear function also passes through point (3,3), and it's graph is sketched at the end of the answer.
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1000 yards is how many inches
Answer:
36000 inches
Step-by-step explanation:
Chris bought 18.4 gallons of gasoline. There are approximately 3.8 liters in 1 gallon.
Which measurement is closest to the number of liters of gasoline Chris bought?
14.6 L
6.21 L
69.92 L
4.84 L