Using a linear function, it is found that he drove the truck for 240 miles.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Researching the problem on the internet, there was a base fee of $18.99, which is the y-intercept, and there was an additional charge of 75 cents for each mile driven, which is the slope, hence the cost function for m miles driven is given by:
C(m) = 18.99 + 0.75m.
He paid $199, hence the number of miles he drove is found as follows:
C(m) = 18.99 + 0.75m.
199 = 18.99 + 0.75m
m = (199 - 18.99)/0.75
m = 240 miles.
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The graph of a function f is shown below.
Find f(-2) and find one value of x for which f(x)=-1.
Answer:
f(-2) = 3, f(0, -3) = -1
Giving brainliest! :)
Answer:
1.39b + 2.49m = 50.73
1.29b + 2.69m = 51.63
Step-by-step explanation:
Systems of linear equations are used when we have 2 equations that both contain 2 unknown variables. Since we are trying to find the price of bread and milk, we can let b = num of bread and m = num of milk.
Betty spends $50.73 buying b loaves of bread and m gallons of milk, so the first equation would be 1.39b + 2.49m = 50.73. Betty spends $51.63 buying b loaves of bread and m gallons of milk at Store B, so the second equation is 1.29b + 2.69m = 51.63.
Algebra help! 1 question
I don’t know the answer and I need help asap
Answer:
The answer is
[tex]a \sin(theta) [/tex]
Step-by-step explanation:
The solution is in the image
A list of positive and negative numbers are in A2 through A400, and the square root of the absolute value is needed for each cell. Which function typed into B2 and copied through B400 will provide this information?
a.
=A2^(1/2)
b.
=SQRT(A2)
c.
=SQRT(ABS(A$2))
d.
=SQRT(ABS(A2))
Answer:
d. =SQRT(ABS(A2))
Step-by-step explanation:
A spreadsheet will not tell you the square root (or half power) of a negative number. It only performs math using real numbers.
ConsiderationsTrying to take a square root of a negative number will result in a #NUM! error being shown in the result cell. Assuming you want the root of the magnitude of the numbers in column A, the value you want the root of is ABS(A2).
Using a dollar sign on a cell reference renders that portion of the cell reference fixed when the formula is copied. Referencing cell A$2 will mean you will get 399 copies of the square root of the contents of cell A2 in cells B2 through B400.
FormulaThe formula that will give you the square root of the magnitude of the adjacent cell in column A will be
=SQRT(ABS(A2)) . . . . . . . . . formula for cell B2, copied to cells below
On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform B and zip to the other platform. What is the coordinate when you reach half way?
he midpoint between the Platform B and C is ( )
, ( )
The coordinates of the mid-point between points B and C is given by:
(-5, -10).
What is the mid-point concept?The mid-point between two points is the halfway point between them, and is found using the mean of the coordinates.
The points in this problem are given as follows:
B(-40, -30), C(30, 10)
Hence the coordinates of the mid-point are:
x = (-40 + 30)/2 = -5.y = (-30 + 10)/2 = -10.More can be learned about the mid-point at https://brainly.com/question/10956693
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Could someone help me out?
Since the grade of the numerator and the denominator is the same, then the limit exists and is distinct from 0. The limit of the expression is 4/7.
How to determine the limit of a rational expression when x tends to infinite
In this problem we must apply some algebraic handling and some known limits to determine whether the limit exists or not. The limit exists if and only if the result exists.
[tex]\lim_{x \to \infty} \frac{4\cdot x - 1}{7\cdot x + 3}[/tex]
[tex]\lim_{x \to \infty} \frac{4\cdot x - 1}{7\cdot x + 3} \cdot \frac{x}{x}[/tex]
[tex]\lim_{x \to \infty} \frac{4 - \frac{1}{x} }{7 + \frac{3}{x} }[/tex]
[tex]\lim_{x \to \infty} \frac{4}{7}[/tex]
4/7
Since the grade of the numerator and the denominator is the same, then the limit exists and is distinct from 0. The limit of the expression is 4/7.
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A data set contains an independent and a dependent variable. Which must be true of the data set if a linear function can
be used to represent the data?
O The set must have a constant additive rate of change.
The set must have a constant multiplicative rate of change.
O The values in the set must be positive.
O The values in the set must be increasing.
Mark this and return
Save and Exit
Next
Submit
The answer choice which must be true regarding the linear function is; The set must have a constant additive rate of change.
Which is true about a linear function?Since a linear function typically takes the slope-intercept form; f(x) = mx +c.
It therefore follows that the equation must have a constant slope m, which is the described additive constant rate of change.
It therefore follows that, the answer choice which is true regarding the linear function is therefore; The set must have a constant additive rate of change.
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Please explain for what values of x is function g(x) continuous if it is defined by.
Using the continuity concept, it is found that the function is continuous for all real values.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In this problem, we are given a piece-wise function, hence we have to look at the points where the definition of the function changes. In this problem, it can only be discontinuous at x = 0, which we have to verify.
Then:
[tex]f(0) = 0^2 - 1 = -1[/tex].[tex]\lim_{x \rightarrow 0^-} = \lim_{x \rightarrow 0} x^2 - 1 = 0^2 - 1 = -1[/tex].[tex]\lim_{x \rightarrow 0^+} = \lim_{x \rightarrow 0} \frac{1}{x - 1} = \frac{1}{0 - 1} = -1[/tex].The 3 values are equal, hence the function is continuous at x = 0 and for all real values.
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A _______________ can be used to display an interval of values from a data set.
A. dot plot
B. any of these
C. bar graph
D. histogram
Answer:
The histogram
The histogram is a popular graphing tool. It is used to summarize discrete or continuous data that are measured on an interval scale. It is often used to illustrate the major features of the distribution of the data in a convenient form.
Hope it helps :)
Answer:
D. Histograph can be used to display an interval of values from a data set
Which of the following examples illustrates ordinal numbers?
A. Marie counted the number of chips on her plate and said, "I have eight".
B. Gracie told Bradly she would be the first one to go down the slide.
C. Bennett said he had more blocks than anyone.
An ordinal number is a number that specifies how something ranks in respect to other numbers. The correct option is B.
What is an ordinal number?An ordinal number is a number that specifies how something ranks in respect to other numbers, such as first, second, third, and so on. This order or sequence might be determined by size, importance, or chronology.
The example that illustrates the ordinal number is "Gracie told Bradly she would be the first one to go down the slide".
Hence, the correct option is B.
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A Standard number is
tossed find each
Probability.
P (4 or less than 6)
the probability of rolling 4 or a number less than 6 is P = 5/6
How to find the probability?The standard number cube has the outcomes {1, 2, 3, 4, 5, 6}
We want to find the probability of rolling 4 or a number less than 6. (4 is a number less than 6).
The outcomes that meet that condition are:
{1, 2, 3, 4, 5}
So 5 out of 6 outcomes meet the condition, then the probability is:
P(4 or less than 6) = 5/6
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Two sublings are 55 years combined and one sibling is 9 years younger how od is the younger sibing
Answer:
23 years old
Step-by-step explanation:
Let x = age of younger sibling.
Then, the age of the older sibling is x + 9.
x + x + 9 = 55
2x = 46
x = 23
Answer: 23 years old
The graph shows the velocity f(t) of a runner during a certain time interval:
Graph of line segment going through ordered pairs 0, 2 and 6, 8. Graph of another line segment going through ordered pairs 6, 8 and 8, 0. Label on the x axis is time in seconds, and label on the y axis is velocity in meters per second.
Which of the following describes the intercepts on the graph?
The initial velocity of the runner was 8 m/s, and the runner stopped after 2 seconds.
The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds.
The initial acceleration of the runner was 8 m/s2, and the runner stopped after 2 seconds.
The initial acceleration of the runner was 2 m/s2, and the runner stopped after 8 seconds.
Answer:
Option B
Step-by-step explanation:
(0,2)(6,8)(8,0)Slope
m=8-2/6m=6/6=1And
m=0-8/8-6m=-8/2m=-4These are acceleration
Y intercept is (0,2) as x coordinate is 0
This is initial velocity 2m/s
The runner stopped at 8s
Find the slope of the line that contains the points (-8, -2) and (-17, 4).
[tex]\Large\maltese\underline{\textsf{A. \space What is Asked}}[/tex]
Find the slope of the line that contains the points (-8,-2) and (-17,4)
[tex]\Large\maltese\underline{\textsf{B.\space This problem has been solved!}}[/tex]
If we are given two points, we can easily find the slope of the line that passes through the points. With points (y₂, y₁) and (x₂, x₁), the slope is [tex]\bf{\dfrac{y2-y1}{x2-x1}[/tex].
Similarly, with points (-8,-2) and (-17,4) the slope is.
[tex]\bf{\dfrac{4-(-2)}{-17-(-8)}}[/tex] | as we can see, it is possible to simplify this further
[tex]\bf{\dfrac{4+2}{-17+8}}[/tex] | simplify
[tex]\bf{\dfrac{6}{-9}[/tex] | reduce
[tex]\bf{-\dfrac{2}{3}}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=-\dfrac{2}{3}}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
Using the equation of slope of a line, the slope of the line that have the given coordinates is -2/3
What is the slope of the line?The slope of a line represents the measure of how steep the line is, or the rate at which the line rises or falls as you move along it. It is calculated as the ratio of the vertical change (change in y-coordinates) to the horizontal change (change in x-coordinates) between any two points on the line.
If you have two points on a line, (x₁, y₁) and (x₂, y₂), the slope (m) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values into the formula above;
m = 4 - (-2) / -17 - (-8)
m = 4 + 2 / -17 + 8
m = 6 / -9
m = -2/3
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if one of two integers is 5% of the other, and their sum is 63, what is their product
Answer:
180
Step-by-step explanation:
Let x be the first integer.
Let y be the 2nd integer.
Given info from the question,
x = 5% x y
x = 0.05y - equation 1
x + y = 63 - equation 2
Lets now substitute equation 1 into equation 2.
0.05y + y = 63
1.05y = 63
y = 63 / 1.05
= 60
Now we substitute y into equation 1.
x = 0.05(60)
= 3
Now since we know both x and y,
we can find the product of them.
xy = 60 * 3 = 180
What is the slope of a line perpendicular to the line whose equation is 3x+3y=18
Step-by-step explanation:
the slope of a line is always the factor of x, when the line is in the form
y = ...
so,
3x + 3y = 18
3y = -3x + 18
y = -x + 6
the slope is -1 = -1/1
as the slope is the ratio of y coordinate change / x coordinate change.
a perpendicular slope switches x and y upside-down and flips the sign.
so, in our case the perpendicular slope is
1/1 = 1
Find the value of x in circle O.
49°
X
Which description best compares the graphs given by the equations: x-5y=-5 5x-25y=75
Considering the slopes of the given lines, they are parallel lines.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.The first line, in standard form, is given by:
5y = x + 5
y = 0.2x + 1.
The slope is of m = 0.2.
For the second line, we have that:
25y = 5x - 75
y = 0.2x - 3
The slope is of m = 0.2.
Same slope, hence the lines are parallel.
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In the diagram, the length of segment VS is 39 units.
T
6x-3
R
56
S
3x + 4
2x + 5
What is the length of segment TV?
O14 units
19 units
38 units
50 units
The measure of TV from the figure is 38 units
Properties of a kite?The given diagram in question is a kite. From the figure, the expression below is true;
6x - 3 = 39
Determine x
6x = 42
x= 7
TV = 2(2x+5)
TV = 2(2(7)+5)
TV = 2(19)
TV = 38 units
Hence the measure of TV from the figure is 38 units
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Classify each sequence as arithmetic, geometric, or neither by dragging it into the correct box.
The sequences are classified, respectively, as:
Geometric, Arithmetic, Neither.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
In the first sequence, we have that:
[tex]q = \frac{45}{15} = \frac{15}{5} = \frac{5}{\frac{5}{3}} = \frac{\frac{5}{3}}{\frac{5}{9}} = 3[/tex]
Hence it is a geometric sequence.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
In the second sequence, we have that:
d = -4 - 1 = 1 - 6 = 6 - 11 = 11 - 16 = -5
Hence it is an arithmetic sequence.
What about the third sequence?[tex]\frac{4}{3} \neq \frac{3}{2}, 1 - \frac{1}{2} \neq 2 - 1[/tex]
Hence it is neither arithmetic nor geometric.
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Dante has scored 30, 18, and 28 points in his three basketball games so far. How many points does he need to score in his next game so that his average (mean) is 26 points per game
Answer:
28
Step-by-step explanation:
Givens
Game 1: 30
Game 2: 18
Game 3: 28
Game 4: x
Solution
(30 + 18 + 28 + x) / 4 = 26 Multiply both sides by 4
4* (30 + 18 + 28 + x) / 4 = 26 * 4 The 4s on the left cancel
30 + 18 + 28 + x = 104 Add the 3 other numbers together
76 + x = 104 Subtract 76 from both sides.
76-76+x = 104-76 The 76s on the left disappear.
x = 28
Answer
in the next game he must score 28 points to average 26
NO LINKS!!! Please help me with this problem
n=3
-2 and 7 + 4i are zeroes;
f(1)= 156
f(x)=
(type an expression using x as the variable. simplify your answer)
Answer:
[tex]f(x)=x^3-12x^2+37x+130[/tex]
Step-by-step explanation:
So I'm assuming when you provided n=3, that means the degree is 3? So the first thing to know, is you can express a polynomial using it's factors as: [tex]f(x)=a(x\pm b)(x\pm b)(x\pm c)[/tex] where the sign of each factor depends on the sign of the factor... the point is it can be either. Notice the a? This usually will determine the stretch/compression of the polynomial, since sometimes the factors will have a coefficient for the x, but in this case I'm assuming all the coefficients of x are 1. So the next thing that is vital to know is that imaginary solutions come in conjugates. This means that if you have a zero at: [tex]a-bi \text{ then }a+bi \text{ is also a zero}[/tex]. So this means you have the 3 zeroes at x=-2, x=7+4i, x=7-4i. These are all the zeroes of the polynomial, since the Fundamental Theorem of Algebra states that a polynomial with degree n will have n solutions, which can be complex or real.
So the factor isn't going to be written as (x-2), it's going to be (x+2) since when you plug in -2 as x, it makes x+2 equal to 0.
The same thing applies for the two imaginary factors, so you're going to have the other two factors as (x-(7+4i)) and (x-(7-4i). You can instead think of it as ((x-7)+4i) and ((x-7)-4i) and you can use the difference of squares identity: [tex](a-b)(a+b)=a^2-b^2[/tex] where in this case a=x-7 and b=4i
So this gives you the equation: [tex]((x-7)-4i)((x-7)+4i) = (x-7)^2-(4i)^2[/tex]
Which becomes: [tex](x^2-14x+49)-16(-1) = x^2-14x+49+16 = x^2-14x+65[/tex]
So this gives us one of the factors: [tex]x^2-14x+65[/tex]
Now plug this in with the other factor and we get the equation:
[tex]f(x) = a(x+2)(x^2-14x+65)[/tex]
Now plug in 1 as x and make f(x) = 156, to solve for a
[tex]156=a(1+2)(1^2-14(1)+65)\\156=a(3)(1-14+65)\\156=a(3)(52)\\156=152a\\a=1[/tex]
So in this case, a=1, so that last step wasn't necessary, although I would check each time just in case a =/= 1.
Original equation
[tex]f(x) = (x+2)(x^2-14x+65)[/tex]
Multiply
[tex]f(x)=(x^3-14x^2+65x)+(2x^2-28x+130)\\[/tex]
Combine like terms:
[tex]f(x)=x^3+(-14x^2+2x^2)+(65x-28x)+130[/tex]
add like terms:
[tex]f(x)=x^3-12x^2+37x+130[/tex]
Answer:
[tex]f(x)=x^3-12x^2+37x+130[/tex]
Step-by-step explanation:
Complex Conjugate Theorem
For a polynomial p(x) with real coefficients, the complex zeros occur in conjugate pairs. So if (a + bi) is a zero, then its conjugate (a - bi) is also a zero.
Given zeros:
-2 and (7 + 4i)
As one of the given zeros is a complex number, (7 - 4i) is also a zero.
Write each zero as part of a factor and multiply them together, adding a leading coefficient [tex]a[/tex]:
[tex]\begin{aligned}f(x) & = a(x+2)(x-(7+4i))(x-(7-4i))\\& = a(x+2)(x-7-4i)(x-7+4i)\\& = a(x+2)(x^2-7x+4ix-7x+49-28i-4ix+28i-16i^2)\\& = a(x+2)(x^2-14x+49-16i^2)\end{aligned}[/tex]
Remember that [tex]i^2=-1[/tex], therefore:
[tex]\begin{aligned}f(x) & = a(x+2)(x^2-14x+49-16(-1))\\& = a(x+2)(x^2-14x+49+16)\\& = a(x+2)(x^2-14x+65)\end{aligned}[/tex]
To find the value of the leading coefficient (a), use the given [tex]f(1)=156[/tex] :
[tex]\begin{aligned}f(1) & = 156\\\implies a(1+2)(1^2-14(1)+65) & = 156\\a(3)(52) & = 156\\156a & = 156\\\implies a & = 1\end{aligned}[/tex]
Therefore, the polynomial in factored form is:
[tex]f(x)=(x+2)(x^2-14x+65)[/tex]
Finally, expand the brackets:
[tex]\begin{aligned}f(x) & =(x+2)(x^2-14x+65)\\& = x^3-14x^2+65x+2x^2-28x+130\\& = x^3-14x^2+2x^2+65x-28x+130\\& = x^3-12x^2+37x+130\end{aligned}[/tex]
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Which ordered pairs are solution to the system of inequalities? {X+2y>4, 3x-y<2
The ordered pairs which is the solution of the system of Inequalities is;
x > 0 and y < 2
How to find the ordered pair of inequalities?We are given the inequalities;
x + 2y > 4 ----(1)
3x - y < 2 -----(2)
Subtract 2y from both sides in eq 1 to get;
x > 4 - 2y ----(3)
Put 4 - 2y for x in eq 2 to get;
3(4 - 2y) - y < 2
12 - 4y - y < 2
12 - 5y < 2
Subtract 12 from both sides to get;
-5y < -10
Divide both sides by -5 to get;
y < 2
Put 2 for y in eq 3 to get;
x > 4 - 2(2)
x > 0
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Complete the equation of the line through ( − 10 , − 7 ) (−10,−7)left parenthesis, minus, 10, comma, minus, 7, right parenthesis and ( − 5 , − 9 ) (−5,−9)left parenthesis, minus, 5, comma, minus, 9, right parenthesis. Use exact numbers.
The equation of the line that passes through (-10,-7) and (-5,-9) is y=-2.5x-31.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The slope of the line is,
Slope, m = (-10+5)/(-7+9) = -5/2 = -2.5
Substitute any one of the points in the equation of the line,
-7 = -2.5(-10) + C
-7 = 25 + C
C = -31
Hence, the equation of the line that passes through (-10,-7) and (-5,-9) is y=-2.5x-31.
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Answer: the answer is y = - 2/5x - 11
Step-by-step explanation:
it’s correct on khan academy
A shelf can be packed from end to end with 30 large books or 45 small books.
Kevin already packed the shelf with 3 large books and 23 small books.
At most, how many more large books can Kevin pack the shelf with?
Ans:
Answer:
11
Step-by-step explanation:
since 30÷45 = 2/3 then
The space taken by a small book is equal to
the space taken by 2/3 a large book.
…………………………………………………
Calculating the number of large book corresponding to 23 small books :
= 23×(2÷3) + 3
= 18.333333333333 (large book)
Then ,Kevin can pack the shelf with (at most) : 30 - 19 = 11 more large books
Add 7 2/3+4/7 reduce to the lowest terms
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{7 \dfrac{2}{3} + \dfrac{4}{7}}[/tex]
[tex]\huge\textbf{Solving:}[/tex]
[tex]\mathbf{7 \dfrac{2}{3} + \dfrac{4}{7}}[/tex]
[tex]\mathbf{= \dfrac{7\times3+2}{3} + \dfrac{4}{7}}[/tex]
[tex]\mathbf{= \dfrac{21 + 2}{3} + \dfrac{4}{7}}[/tex]
[tex]\mathbf{= \dfrac{23}{3} + \dfrac{4}{7}}[/tex]
[tex]\mathbf{= \dfrac{173}{21}}[/tex]
[tex]\mathbf{\approx 8 \dfrac{5}{21}}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathsf{8 \dfrac{5}{21}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
[tex]8\frac{5}{21}[/tex]
Step-by-step explanation:
[tex]7\frac{2}{3} +\frac{4}{7} = 7\frac{14}{21} +\frac{12}{21} = 8\frac{5}{21}[/tex]
If a pool deck of 650 square feet is to be laid with concrete 3" thick, what volume of concrete will have to be poured in cubic yard? ( round to the nearest cubic yard)
Volume is a three-dimensional scalar quantity. The volume of concrete that will have to be poured into the pool deck is 6.0185 cubic yards.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Since an inch is equal to 1/12 of a foot. Therefore, the thickness of the pool deck is,
3 inches = 0.25 foot
If a pool deck of 650 square feet is to be laid with concrete 3" thick, then the volume of concrete that will be needed is,
Volume of concrete = 650 ft² × 0.25 ft = 162.5 ft³
Now, one yard is equal to 3 feet, therefore,
1 cubic foot = 1/27 cubic yards
162.5 cubic feet = 6.0185 cubic yards
Hence, the volume of concrete that will have to be poured into the pool deck is 6.0185 cubic yards.
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Use the function below to find F(1)
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
plug 1 in for t
[tex]F(t)=4(\frac{1}{2^3^t})\\ F(1)=4(\frac{1}{2^3^*^1})\\ F(1)=4(\frac{1}{2^3})\\ F(1)=4(\frac{1}{8})\\ F(1)=\frac{4}{8} \\F(1)=\frac{1}{2}[/tex]
Can you help me to answer the question
Answer:
I'm not too sure but:
L = (-2,-3)
M = (-9,-3)
K = (-2,-8)
J = (-9,-8)
Step-by-step explanation:
What we know:
We know that we go through the x axis then the y axis hence the saying "Along the corridor, Up the stairs".
Due to us knowing this we use where the letters (L, M, K & J) are placed on the diagram and use the "Along the corridor, Up the stairs" technique to figure out the answer.
This means that L is (-2,-3), M is (-9,-3), K is (-2,-8) & J is (-9,-8).
Yet again as I said at the top i'm not too sure but this is what I think is correct.
I hope it helps! :)