The total number of employees in the company in the year 2015 is 275 employees
Number of employees in the company before increase = 200 employees
Percentage increase in employees between 2005 and 2010 = 25%
Percentage: A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test.
So, the number of employees after the increase = 200+25%of 200
= 200+50 = 250
Percentage increase in employees between 2010 and 2015 = 10%
Number of employees after increase = 250 + 10% of 250
= 250 + 25 = 275 employees
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Question 8A: Mr. Sowers wants to purchase expo markers for his classroom. He has a budget of $35. A four pack of markers costs $5.49, including tax. Write and solve an inequality, using x for the variable, to solve for the number of packs of markers Mr. Sowers can purchase. Copy/paste one of the following inequality symbols to help you write your inequality: ≤ < ≥ >
The number of packs of markers that Mr. Sowers can purchase is 6.
How many packs can he buy?The maximum amount that Mr. Sowers can spend is $35. This means that the amount can either by $35 or less than $35. Thus, the inequality sign that would be used is the less than or equal to sign, ≤ .
total amount spent on the packet of markets ≤ budget
(cost of one packet x number of packets) ≤ $35
$5.49x ≤ $35
In order to determine the value of x, divide both sides of the equation by 5.49
x ≤ $35 / 5. 49
x ≤ 6.38
x ≤ 6
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rewrite 5+3/4x=3/8 so it doesn't have fractions
Answer:
40 + 6x = 3
Step-by-step explanation:
Multiple all the way through by 8
8( 5 + [tex]\frac{3}{4}[/tex] x) = ([tex]\frac{3}{8}[/tex])8
8(5) + [tex]\frac{8}{1}[/tex][tex](\frac{3}{4})[/tex]x = [tex]\frac{3}{8}[/tex][tex](\frac{8}{1})[/tex]
40 + 6x = 3
The slope of the trend line is 15 what does that mean in regards to the data of the scatter plot? Check all that apply
The correct options are-
1. The slope represents the rate of change of the data.
3. Sales increase $1,000 as ads increase by $1,000.
5. A positive slope infers a positive correlation.
What is defined as the slope?The slope of a line measures its steepness as well as direction.The slope of a line is defined as the change throughout y coordinate in relation to the transformation in x coordinate.The net change in y coordinates is y, while the net change in x coordinates is x.So m represents the transition in y coordinate throughout relation to the shift in x coordinate. m = Δy/Δx, where, m is the slope.Positive correlation:
A positive correlation is a correlation that exists between two variables which move in the same direction. A positive correlation exists whenever one variable decreases while the other increases, or when one variable increases whereas the other decreases.From the scatter points on graph, its clear that the slope which is 15 is a positive correlation.
Now, to find the slope we see the change in y with respect to x.
Thus, the change in sales increase $1,000 as ads increase by $1,000.
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The complete question is-
The slope of the trend line is 15. What does that mean in regard to the data of the scatterplot? Check all that apply.
1. The slope represents the rate of change of the data.
2. Advertising costs increase $1,000 as sales increase by $1,000.
3. Sales increase $1,000 as ads increase by $1,000.
4. A positive slope infers a negative correlation.
5. A positive slope infers a positive correlation.'
Rearrange the equation
a= 1/4 b
to make b the subject.
b = 4a is the answer.
How to make b a subject?Given,
a= 1/4 b
To find:
Make b the subject, the given equation
Solution:
Take 4 to the side of a
4a = 1b
Therefore,
b = 4a
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Point C is on line segment \overline{BD} BD . Given CD=11 CD=11 and BD=17,BD=17, determine the length \overline{BC}. BC
Answer:
draw the diagram out
Step-by-step explanation:
BC=17-11
= 6
20 POINTS!
Please Help Me!
What is the equation of the line perpendicular to -2x + 3y = -12 and which passes through the point (2, -5)? Write your answer in slope-intercept form. Show all your work.
Explanation:
the equation of a line in
slope-intercept form
is.
∙
x
y
=
m
x
+
b
where m is the slope and b the y-intercept
rearrange
2
x
−
3
y
=
12
into this form
subtract 2x from both sides
⇒
−
3
y
=
−
2
x
+
12
divide all terms by
−
3
⇒
y
=
2
3
x
−
4
←
in standard form
with
m
=
2
3
given a line with slope m then the slope of a line
perpendicular to it is
∙
x
m
perpendicular
=
−
1
m
⇒
m
perpendicular
=
−
1
2
3
=
−
3
2
⇒
y
=
−
3
2
x
+
b
←
is the partial equation
to find b substitute
(
2
,
6
)
into the partial equation
6
=
−
3
+
b
⇒
b
=
6
+
3
=
9
⇒
y
=
−
3
2
x
+
9
←
equation of perpendicular line
a bacteria doubles every day. Write an expression to show how many bacteria will be there after 10 days. Assume there were 175 bacteria at beginning
Answer:
175 x 20
Step-by-step explanation:
You said that bacteria doubles every day, so it's x2. Since it's the course over 10 days, it's 10 x 2 = 20. So the expression is 175 x 20.
Y=x^2+5x-3
Y-x=2
What is the solution to the linear-quadratic system of equations.
The solution to the linear-quadratic system of equations are: [tex]\begin{pmatrix}x=1,\:&y=3\\ x=-5,\:&y=-3\end{pmatrix}[/tex].
Quadratic Function
The Standard form for a quadratic equation is ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
To solve a quadratic function, you should find the discriminant: D=b²-4ac and then use this variable in the formula: [tex]x=\frac{-b\±\sqrt{\Delta} }{2a}[/tex].
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=4x+3. Where:
m= the slope. It can be calculated for Δy/Δx .
b= the constant term that represents the y-intercept.
The question asks the solution of the system the following equations
y=x²+5x-3 (1)
y=2+x (2)
Firstly, you should subtract equation 1 and 2, as result, you have
y-y= x²+5x-3 -(2+x)
y-y= x²+5x-3 -2 -x
0= x² +4x -5
After that for finding x, you should solve the equation x² +4x -5=0. Then,
D=b²-4ac
D= 4²-4*1*(-5)
D=16+20
d=36
Thus,
[tex]x=\frac{-b\±\sqrt{\Delta} }{2a}= \frac{-4\±\sqrt{36} }{2*1}= \frac{-4\±\ 6 }{2}[/tex]. Therefore
x1=(-4-6)/2= -10/2=-5
x2= (-4+6)/2 = 2/2=1
From equation 2 : y=2+x
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ngth of the third side. If necessary, write in simplest radical form.
5
V11
Pythagoras theorem - The length of the third side is 6.71unit
What is Pythagoras theorem ?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The Pythagoras theorem's equation is as follows:
H² = P² + B²
The triangle's third side will be the following length:
Let x represent the triangle's third side's length.
9² = 6² + x²
81 = 36 + x²
x² = 45
x = 6.708
x = 6.71 units
Hence, the third side of the triangle is 6.71unit
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Where does the graph of y= -2x + 1 intersect the x-axis?
The graph intersects the x-axis at ( 1/2 , 0) .
A cartesian coordinate system, which uses signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length, uniquely identifies any point in a plane by a pair of numerical coordinates.
The origin of each reference coordinate line, known as an x-axis or y-axis of the system or simply an axis (plural axes), is the intersection of the ordered pairs (0, 0).The coordinates can also be determined by looking at the locations of the perpendicular projections of the point onto the x- axis and y -axis, which are shown as signed distances from the origin.We know that at the x-axis the value of y is 0 .
Now substituting the value of y in the equation of the graph we get :
y = - 2x + 1
at y = 0 ,
0 = -2x + 1
or, -1 = -2 x
or, x = 1 / 2
Hence the co-ordinate of the point where the graph passes through x-axis is ( 1/2 , 0 ) .
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What’s the value of x
Using the rules of complementary angles we calculate that the value of x is 12° .
Pairs of complementary angles have measures which are one right angle.
The non-shared sides of two adjacent complementary angles form a right angle. Given that the sum of a triangle's internal angles is 180 degrees and the right angle alone accounts for 90 degrees, the two sharp angles of a right triangle are complimentary in Euclidean geometry.The Latin word complementum, from which the English word complement is derived, is related to the verb complere, which means "to full up." A right angle is created when an acute angle is "filled up" by its opposite.The complement of the angle describes the distinction between an angle and a straight angle.The two given angles are 29° and ( 5x + 1 )°.
There are a pair of complementary angles.
Therefore 29° + ( 5x + 1 )° = 90 °
or, 5x + 30° = 90 °
or, 5x = 60
or, x = 12°
Therefore using the rules of complementary angles we calculate the value of x is 12°.
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On a coordinate plane, 3 parallelograms are shown. Parallelogram A B C D has points (3, 5), (6, 5), (4, 1), (1, 1). Parallelogram A prime B prime C prime D prime has points (3, negative 5), (6, negative 5), (4, negative 1), (1, negative 1). Parallelogram A double-prime B double-prime C double-prime D double-prime has points (negative 3, negative 4), (0, negative 4), (negative 2, 0), (negative 4, 0).
Which rule describes the composition of transformations that maps pre-image ABCD to final image A"B"C"D"?
Reflection across the x-axis composition translation of negative 6 units x, 1 unit y.
Translation of negative 6 units x, 1 unit y composition reflection across the x-axis.
90 degree rotation about point 0 composition translation of negative 6 units x, 1 unit y.
Translation of negative 6 units x, 1 unit y composition 90 degree rotation about point 0.
Translation of negative 6 units x, 1 units y composition reflection across the x-axis
The composition transformation that maps ABCD to A''B''C''D'' comprises
of two or more transformations that maps the image
The rule that describes the composition transformation that maps ABCD to
A''B''C''D'' is the option;
Translation of negative 6 units x, 1 units y composition reflection across the x-axis.
The given coordinates of parallelogram ABCD are (3, 5), (6, 5), (4, 1), (1, 1)
The coordinates of the parallelogram A'B'C'D' are; A'(3, -5), B'(6, -5), C'(4, -1), D(1, -1)
The coordinates of the parallelogram A''B''C''D'' are;
D(-5, 0), C''(-2, 0), A''(-3, -4), B''(0, -4)
The image of the point (x, y), following a reflection about the x-axis is the point (x, -y)
The difference in the coordinates of the parallelogram ABCD and A'B'C'D'
is the change in the sign of the y-coordinates
Therefore, the transformation that gives the parallelogram A'B'C'D' from
the parallelogram ABCD is a reflection about the x-axis
The difference between the coordinates of the vertices of the
parallelogram A'B'C'D' and the parallelogram A''B''C''D'', is a change in the
x-value by (-6), and a change in the y-value by (+1)
Therefore, the parallelogram A''B''C''D'' can be obtained from parallelogram
A'B'C'D', by a translation of -6 units (left) in the x-direction and a translation
of 1 unit, x in the y-direction
Which gives;
The composition transformation that maps the pre-image ABCD to the
final image A''B''C''D'', (given that in a composition transformation, the
transformation to the right is done first) are;
[tex]$\mathrm{T}_{-6,1} \cdot \mathrm{r}_{\mathrm{x}-\{axis}}(\mathrm{x}, \mathbf{y})$[/tex]which is the option;
Translation of negative 6 units x, 1 units y composition reflection across the x-axis
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help please with this question
About Nevada state, it is true that "The rural air pollution level for this state is much higher or much lower than the rest of the states in the data set."
The researcher has collected the data on the air pollution levels, measured in milligrams per cubic meter, for both urban and rural areas in 35 states.The data is plotted with urban air pollution levels on the horizontal axis and rural air pollution levels on the vertical axis.Nevada is an outlier in the y-direction.This clearly shows that "the rural air pollution levels for this state are much higher or lower than the rest of the states in the data set".To learn more about outliers, visit :
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HELP PLEASEEEE!!!!!!!!
Answer:
a) ¹⁰√4
Step-by-step explanation:
(4 ⅖)¼ = 4 ^ 2/5 × 1/4 = 4^ 2/20 on simplifying further we get answer as a
What is the sequence of transformations that maps ABC to A’B’C’
Step 1:
A. Reflect across the line Y=X
B. Reflect across the x-axis
C. Rotate 90° clockwise about the origin.
D. Rotate 180° about the origin
Step 2:
A. Translate 6 units up
B. Translate 5 units up
C. Reflect across the line y=x
D. Reflect across the x-axis
The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line y = x followed by a translation 10 units right and 4 units up.
What is meant by the sequence of transformations?A certain order of transformational occurrences is referred to as a transformational sequence. This indicates that more than one transformation is handled by a series of transformations, and the order in which they happen is important.
We are given that ΔA'B'C' exists formed after a sequence of transformations applied to ΔABC.
The first exists a reflection across a line and the second exists a translation.
The coordinates of point C exist (-4, -2). After reflection from the line y = x, the coordinates become (2, -4).
Also, the coordinates of point C' are (12, 0).
So, to get point C' from point C, we should add 10 units to the x-coordinate and 4 units to the y-coordinate.
The translation of 10 units right and 4 units up.
Therefore, the complete transformation is
The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line y = x followed by a translation 10 units right and 4 units up.
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A new hospital in Stamford starts out with 10 junior residents and 5 senior residents on its staff. Management plans to hire additional personnel at a rate of 2 junior residents per month and 3 senior residents per month. Eventually, there will be an equal number of each on the hospital staff. How many of each type will there be?
NEED HELP ON THE GRAPH AS WELL
Question
Refer to the Newsela article, "Doctoral Student Played a Big Part in First Black Hole Photo."
How does Bouman contribute to taking the first photograph of a black hole?
Responses
Bouman is the first person to suggest that black holes exist in space.
Bouman invents a telescope that can gather images taken by eight telescopes located around the world.
She and her team create an algorithm that makes it possible to collect data and combine it into one image.
Her TED talks on black holes inspire other scientists to figure out how to photograph them.
Bouman contributed to taking the first photograph of a black hole as she and her team created an algorithm that makes it possible to collect data and combine it into one image.
What facts are drawn from Newsela article?The article highlighted the importance of Katie Bouman in leading her team who created a computer software capable of using an algorithm that analyzes data and creates an image based on it. Its elaboration took about two years to complete but the results were very promising and promoted a great advance for science.
In conclusion, Bouman and the team were able to develop series of algorithms that converted telescopic data into the historic photo shared by the world's media.
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What value of x would result in the numerical value of zero in the expression -10+11+x
Answer:
-1
Step-by-step explanation:
-10+11+x = 0
1+x = 0
x = -1
what is 7 1/5 divided by 8 in fraction form and as a mixed number
7 1/5 divided by 8 in fraction form is 36 / 40 = 9/ 10 and in decimal form = 0.9
A fraction is a numerical expression expressing a portion of the whole. There are two parts: a numerator and a denominator. The denominator is the total number of pieces that make up the whole, while the numerator is the number of equally sized portions of the whole. For instance, in the percentage of 3/8 has a denominator of 8 and a numerator of 3.
We have been given that -
7 1/5 divided by 8
Rewrite as
(36/5) / 8
36 / 5×8
Multiplying 5 with 8 and we get
36 / 40
Follow these steps to convert an incorrect fraction to a mixed number: Subtract the denominator from the numerator. The quotient's whole number component should be written down. Write the leftover amount on top of the original denominator.
36/ 40 in decimal form = 0.9
0.9 = 0.9 × 10 /1 × 10
= 9 / 10
Hence, When 7 1/5 is divided by 8, the result is 36/40 (9/10) and 0.9 (in decimal notation).
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prove that (a - b)2 = (b - a)2
Answer:
Step-by-step explanation:
(a - b)² =
(a - b)(a - b) =
[(- 1)(b - a)] × [(- 1)(b - a)] =
(- 1)(- 1)(b - a)(b - a) =
(b - a)²
Make a table of ordered pairs for the equation.
y=−13x+4
Then plot two points to graph the equation.
PLEASE ANSWER QUICKLEY, I WILL GIVE YOU 90 POINTS IF IT IS CORRECT and maybe brainleist
Table of ordered pair for the equation y =-13x +4 is given by (0,4) and (1,-9).
As given in the question,
Given equation is equal to :
y = -13x + 4
Substitute x =0 in the given equation
y = -13 (0) + 4
⇒ y = 0 +4
⇒ y = 4
Ordered pair is (0,4)
Substitute x=1 in the given equation
y = -13(1) +4
⇒ y = -9
Ordered pair is (1,-9)
Table of the ordered pair is
x : 0 1
y : 4 -9
Graph of the two plot points A(0,4) and B(1,-9) attached.
Therefore, table of ordered pair for the equation y =-13x +4 is given by (0,4) and (1,-9).
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Ivan was at the beach. He wanted to spend $12 or less on a beach bike rental. The company he chose
to rent from charged an initial fee of $5 and an additional $0.45 per mile he rode.
a. Write an inequality for this situation. Let x represent the number of miles ridden.
b. What is the greatest number of whole miles Ivan can ride without going over his spending
limit?
Using a linear function, it is found that:
a. The inequality for this situation is: 5 + 0.45x ≤ 12.
b. He can ride at most 15 miles without going over the limit.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which the coefficients are described as follows:
The coefficient 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.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).For the context of this problem, the slope and the intercept are defined as follows:
The slope is the cost per mile, hence m = 0.45.The intercept is the flat cost, the renting fee of b = 5.Hence the cost function, considering x miles, is given as follows:
C(x) = 0.45x + 5.
He wanted to spend $12 or less on a beach bike rental, hence the inequality that models this situation is given by:
C(x) ≤ 12.
5 + 0.45x ≤ 12.
The inequality is solved similarly to an equality, isolating the variable and finding the range of values, hence the solution is found as follows:
0.45x ≤ 7
x ≤ 7/0.45
x ≤ 15.6 miles.
The greatest whole number of miles is of 15 miles, as for 16 miles, the cost would be above $12.
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Both Felipe and Enzo forgot to study for their science test. The probability of Felipe passing the test is 0.190.190, point, 19. The probability of Enzo passing the test is \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction. Which of these events is more likely? Choose 1 answer: Choose 1 answer: (Choice A) A Felipe passes the test. (Choice B) B Enzo passes the test. (Choice C) C Neither. Both events are equally likely.
The more likely event is (B) Enzo passes the test , the correct option is (B).
In the question ,
it is given that
the probability that Felipe will pass the test is 0.19
Converting 0.19 to percent , we get
0.19 = 0.19/100 = 19%
the probability that Enzo will pass the test is 1/4 ,
Converting 1/4 to percent , we get
1/4 = 1/4 * 100 = 100/4 =25%
hence , the probability of Felipe passing the test is 19% and the probability that Enzo passes the test is 25% ,
On comparing we see that 25% > 19% , which means Enzo has higher chance of passing the test than Felipe .
Therefore , the more likely event is (B) Enzo passes the test , the correct option is (B).
The given question is incomplete , the complete question is
Both Felipe and Enzo forgot to study for their science test. The probability of Felipe passing the test is .19 , the probability of Enzo passing the test is 1/4.
Which of these events is more likely?
(A) Felipe passes the test.
(B) Enzo passes the test.
(C) Neither. Both event are equally likely.
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what is the value of the expression 3(a+1)-b when a=2 and b= -1
Answer:
it is ten 10
Step-by-step explanation:
4x^-x/x^3-2 how much
Answer:
4x^-x-1
Step-by-step explanation:
4x^-x/x^3-2
= 4x^-x/x
= 4x^-x-1
Evaluate the Expression when x is -9
When is -9, x^2 is [ ]
(Simplify your answer)
Step-by-step explanation:
that only means we need to put the given values into every place, where the variable is used in the expression.
this is straight forward.
x² for x = -9 means
(-9)² = 81
you remember, a² = a×a.
and when a is negative, this is then the multiplication of a negative number with a negative number, and that result is positive.
so, a square operation always delivers a positive result for real numbers as input, no matter if the input was already positive or negative.
you’ve asked for a survey of your property and the surveyor has just sent you a drawing of your property boundary. you show it to your neighbor and he says that the boundary between your two properties is wrong. he says his legal description says that that boundary bears n49°31’56.37""w at 363.591’. he says you shouldn’t pay the surveyor and get him back out to re-survey that line. who is right?
"Seven Year Rule," which is derived from Section 157(4) of the Planning and Development Act 2000, is not the same as this.
What does the seven-year time limit mean?
The so-called "Seven Year Rule," which is derived from Section 157(4) of the Planning and Development Act 2000, is not the same as this. This indicates that once seven years have passed after the start of the development, local authorities cannot issue enforcement notices for an unauthorized development.It is time to speak with a lawyer or the organization that insured your title if there is a sizable discrepancy between where two deeds set a property border. It's possible that a mistake was made when drafting one of the deeds. To try to pinpoint the time the issue happened, someone may need to conduct research on both attributes. The mistake can affect multiple previous landowners.Remember that the majority of surveys indicate the property lines on the deed. Usually, the poll doesn't directly state that a certain action is improper. Ideally, the position of the property line is agreed upon in both documents. Both properties likely once belonged to a bigger tract.Learn more about Seven year rule'
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Draw the graph of f(x)=[[x - 4]] - 2
Answer:
See attachment.
Step-by-step explanation:
Given absolute value function:
[tex]f(x)=|x-4|-2[/tex]
The parent absolute value function is f(x) = |x|.
Graph of the parent absolute value function:
Vertex at (0, 0)|y| = -x if x ≤ 0|y| = x if x ≥ 0Translations
[tex]\textsf{For $a > 0$}:[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
The graph of the given function is a transformation of the parent function by:
Translation of 4 units right.Translation of 2 units down.Therefore, the vertex of the given function is (4, -2).
Find two further points on the graph by inputting x-values either side of the x-value of the vertex into the given function:
[tex]\begin{aligned}\implies f(8)&=|8-4|-2\\&=|4|-2\\&=4-2\\&=2\end{aligned}[/tex]
[tex]\begin{aligned}\implies f(0)&=|0-4|-2\\&=|-4|-2\\&=4-2\\&=2\end{aligned}[/tex]
To draw the graph of the given function:
Plot the vertex (4, -2).Draw a straight line from the vertex through point (8, 2).Draw a straight line from the vertex through point (0, 2).James had pizza delivered. James tips $5 for deliveries or 10% of the purchase, whichever is higher. The pizza delivered cost $69.50.
How much will James tip?
Answer:
Step-by-step explanation:
$4.69
For the function y = x² - 8x + 16, work out the coordinates of the y-
intercept.