Complete the empty table from the provided information.
Transform the graph of f(x) by dilating it by a factor of -2 and then shift it up 3.
Write the equation of the resulting line in slope intercept form.
The empty table should be completed with the coordinates of the transformed graph after a dilation with a scale factor of 3 as follows;
x m(x)
4 -2
2 -1
0 0
-2 1
-4 2
The equation of the resulting line in slope-intercept form is y = -0.5x + 3.
How to transform the graph of f(x) through dilation?Based on the given coordinates of the graph of function f(x), the dilation with a scale factor of 3 from the origin (0, 0) or center of dilation would be calculated as follows:
Point 1 (-2) → Point 1' (-2 × -2) = Point 1' (4).
Point 2 (-1) → Point 2' (-1 × -2) = Point 2' (2).
Point 3 (0) → Point 3' (0 × -2) = Point 3' (0).
Point 4 (1) → Point 4' (1 × -2) = Point 4' (-2).
Point 5 (2) → Point 5' (2 × -2) = Point 5' (-4).
Next, we would translate the graph of function f(x) 3 units up as follows:
Point 1 (-2) → Point 1' (-2 + 3) = Point 1' (1).
Point 2 (-1) → Point 2' (-1 + 3) = Point 2' (2).
Point 3 (0) → Point 3' (0 + 3) = Point 3' (3).
Point 4 (1) → Point 4' (1 + 3) = Point 4' (4).
Point 5 (2) → Point 5' (2 + 3) = Point 5' (5).
Now, we can determine the slope of the transformed graph:
Slope, m = Δy/Δx
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (2 - 1)/(2 - 4)
Slope, m = -1/2 or -0.5
Mathematically, the slope-intercept form of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the y-intercept.At point (2, 2) and y-intercept c = 3, we have:
y = mx + c
y = -0.5x + 3
Read more on dilation here: brainly.com/question/20482938
#SPJ1
ABCD is a rectangle that represents a park. The lines show all the paths in the park. The circular path is in the centre of the rectangle and has a diameter of 10 m. Calculate the shortest distance from A to C across the park, using only the lines shown. B 40 m A 70 m C D
the domain of f(x) = -3x is (0, 1, 2). State the range of f (x) using set notation
The range of the function f (x) = -3x are (0, -3, 6).
What is Domain?
The set of all inputs of the function is called Domain of set.
Given that;
The domain of f(x) = -3x is (0, 1, 2).
Now, Domain of the function are the values of x.
So, We find the Range of the function as;
Substitute all the values of domain (x) in the given function as;
The function is;
f (x) = -3x
For x = 0
Range = f (x) = - 3 × 0 = 0
For x = 1;
Range = f (x) = - 3 × 1 = -3
For x = 2
Range = f (x) = 3 × 2 = 6
Thus, Range of the function are (0, -3, 6)
Therefore, The range of the function f (x) = -3x are (0, -3, 6).
Learn more about the range visit:
brainly.com/question/25962668
#SPJ1
A number, m, rounded to 1 d.p. is 48.2 Another number, n, rounded to 1 d.p. is 6.7 What are the lower and upper bounds of m - n?
The corresponding values of the lower and upper bounds of m - n are 41.41 and 41.59.
What are the values of the lower and upper bounds of m - n?
Upper and lower bounds are the possible maximum and minimum values of a number before it was rounded.
The upper and lower bounds can be expressed using the error interval
The lowest value of m is 48.15
The highest value of m is 48.24
The lowest value of n is 6.65
The highest value of n is 6.74
Therefore, lower bound of m - n = 48.15 - 6.74 = 41.41
Also, the upper bound of m - n = 48.24 - 6.65 = 41.59
So values of the lower and upper bounds of m - n are 41.41 and 41.59 respectively.
Learn more about lower and upper bounds on:
https://brainly.com/question/28154881
#SPJ1
A square and a rectangle have equal perimeters. The length of a side of the square is 2x+1. The length of the rectangle is x+2 and the width is x. Write and solve an equation to find x
When a square and a rectangle have the same perimeters. If the length of a side of the square is 4x-1 and the length of the rectangle is 2x+1 and the width is x+2. then the value of x=1
The perimeter of the square is equal to the perimeter of the rectangle.
The length of a side of the square=4x-1
The perimeter of the square=4a
Where a is the side of the square
Substitute the values in the equation
The perimeter of the square=4(4x-1)=16x-4
The length of the rectangle=2x+1
The width of the rectangle=x+2
The perimeter of the rectangle=2(l+w)
where l is the length and w is the width
The perimeter of the rectangle =2(2x+1+x+2)
=2(3x+3)
= 6x+6
A square and a rectangle have equal perimeters
16x-4=6x+6
16x-6x=6+4
10x=10
x=1
Hence, when a square and a rectangle have the same perimeters. If the length of a side of the square is 4x-1 and the length of the rectangle is 2x+1 and the width is x+2. then the value of x=1
The complete question is
A square and a rectangle have the same perimeters. The length of a side of the square is 4x-1. The length of the rectangle is 2x+1 and the width is x+2, Write and solve an equation to find x
Learn more about perimeter here
brainly.com/question/15287805
#SPJ1
write and simplify a division expression to find the number of cups of flour max needs to use if he has just 1 egg
The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.
1 egg = M/N cups of flour.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Let M cups of flour be needed for N eggs.
This can be written as:
N eggs = M cups of flour
Divide both sides by N.
1 egg = M/N cups of flour
Thus,
The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.
1 egg = M/N cups of flour.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
a red light flashes every 17 seconds
a green light flashes every 15 seconds
they both flash at the same time
after how many seconds will they both flash at the same time?
please help
Answer:
Both the lights will flash 1440 times a day. Proof: Red light flashes after every 30 seconds and green light flashes after every 20 seconds.
Step-by-step explanation:
Please help the Asap the question is in the picture
The length is 16.6ft and the width is 8.9ft
Area of the rectangular area = Length × width
A = LW … 1
What is the explanation?If he wants to have a rectangular area of turf with length one foot less than 3 times the width, then
L = 3W - 1 … 2
Substitute 2 into 1
A = (2W-1)W
A = 2W^2 - W
Since area = 150sq.ft
150 = 2W^2 - W
2W^2 - W - 150 = 0
Factorize
2W^2 - W - 150 = 0
W = 1±√1+4(300)/2(2)
W = 1±√1201/2(2)
W = 1±34.655/4
W = 35.655/4
W = 8.91375
W = 8.9 (to nearest tenth)
Get the length
L = A/W
L = 150/8.9
L = 16.85
L = 16.6ft
Hence the length is 16.6ft and the width is 8.9ft
To learn more about rectangular, refer to:
https://brainly.com/question/25292087
#SPJ13
Round to the nearest thousandth 88.6217
Answer:
88.6000 = 88.622
Shureka Washburn has scores of 69, 74, 79, and 62 on her algebra tests. a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 71 or higher, given that the final exam counts as two tests. b. Explain the meaning of the answer to part (a).
If Shureka Washburn has scores of 69, 74, 79, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71
The scores she scored on test = 69, 74, 79, 62
Consider the final score she must make on the final exam as x
Sum of the scores = 69+74+79+62+2x
= 284+2x
Consider the average of score = Sum of scores / Number of subjects
= (284+2x)/6
She need average of 71 or higher
Then the inequality equation will be
(284+2x)/6 ≥ 71
284+2x ≥ 426
2x ≥ 426-284
2x ≥ 142
x ≥ 71
Hence, if Shureka Washburn has scores of 69, 74, 79, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71
Learn more about inequality here
brainly.com/question/28823603
#SPJ1
Kaylie is 6 years old. Her sister, Amanda is 2x younger. Kaylie is now 36. How old is Amanda?
In a case whereby Kaylie is 6 years old and Her sister, Amanda is 2x younger. Kaylie is now 36 the, Amanda age will now be expressed as 33 years.
How can the age of Amanda be calculated?This implies that when Kaylie is 6 years old then her Her sister, Amanda will be 6/2 = 3 years old.
Then we were told again that Kaylie is now 36, then the age of Amanda will now be (36-3)= 33 years
This is because when Kaylie was 6 years old , she was older by her sisiter by just just 3 years, which is still the same when she grown in age again, the 3 years interval is maintained.
Learn more about expression at:
https://brainly.com/question/1859113
#SPJ1
Evaluate 5(x - 1) - 2 when x = 3.
OA. 8
OB. 0
O C. 12
OD. -4
The value of f(3) for the given expression is 8.
What is evaluation of an expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression. The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given, the expression is 5(x - 1) - 2
Let y = f(x) = 5(x - 1) - 2 = 5x - 5 - 2 = 5x - 7
Therefore, f(3) using the equation above is: f(3) = 5(3) - 7 = 8
Thus, the value of f(3) or y at x = 3 for the given expression is 8.
To learn more about this, tap on the link below:
https://brainly.com/question/4344214
#SPJ9
10 Please help I’ll give brainly
Answer:
11) 7d + 28 and 7(d+4)
12) y^2 + 3y and y(y+3)
Step-by-step explanation:
HELP PLS Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 3p − 10 ≥ 7p + 6 true.
Answer:
{-4; -5}
Step-by-step explanation:
just put any integer from set S in place of p and you will know. the inequality is false with -2 and -3, but with other two numbers is true
ANSWER QUICK FOR BRAINLIEST!!! THREE MATH QUESTIONS!!!
Question 10 (Multiple Choice Worth 2 points)
(One-Step Inequalities MC)
Write the inequality for the statement:
the difference between a number and seven eighths exceeds negative two thirds
f plus 7 over 8 is greater than 2 over 3
f minus 7 over 8 is less than or equal to negative 2 over 3
f minus 7 over 8 is greater than negative 2 over 3
f minus 7 over 8 is less than negative 2 over 3
Question 11 (Multiple Choice Worth 2 points)
(Adding and Subtracting Linear Expressions MC)
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Question 13 (Multiple Choice Worth 2 points)
(Solving Two-Step Equations MC)
Solve the equation for x.
−0.28x − 15.3 = 1.92
x = 61.5
x = −61.5
x = 47.8
x = −47.8
1. The inequality for the statement is C. f minus 7 over 8 is greater than negative 2 over 3
2. The value of the expression is C. 43 over 24 times j plus 1 over 12.
3. −0.28x − 15.3 = 1.92 will be B. -61.5.
What is the inequality?1. The difference between a number and seven eighths exceeds negative two thirds is:
Let the number be f.
This will be:
f - 7/8 > -2/3
2. The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths will be:
= -1/8j + 2/3 - 5/3j + 9/12
= -1/8j - 5/3j + 9/12 - 8/12
= -3/24j - 40/24j + 1/12
= -43/24j + 1/12
3. −0.28x − 15.3 = 1.92
Collect like term
−0.28x = 1.92 + 15.3
-0.28x = 17.22
x = 17.22 /- 0.28
x = -61.5
Learn more about inequalities on:
brainly.com/question/11613554
#SPJ1
When simplified, i⁹⁹ is equivalent to
Complex number :
[tex]i^{99}[/tex]= - i.
Why is it called a complex number?A complex number is one that has the notation a + b I a + bi a+bi, where a and b are real numbers and I is the imaginary unit denoted by the expressions I 2 = 1 I 2 = -1 I 2 = 1. Real numbers (R) and pure imaginary numbers (I) are both included in the set of complex numbers, represented by the letter C.In the 19th century, the phrase "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complicated number that is not real or, more commonly, a number whose real portion is zero (a.k.a "pure imaginary").here,
i = [tex]\sqrt{-1}[/tex]
If the power is
even then the value could be -1 or 1odd then the value could be -i or i99 is odd so now is
-i if (99+1)/2 is even or is
i is (99+1)/2 is odd
Now check (99+1)/2= 100/2= 50,
50 is even so
i^99 = -i
To learn more about : Complex number
Ref : https://brainly.com/question/11175844
#SPJ13
The total surface area of this cuboid is 112 cm². Find the value of x. 10 cm length 2 cm width x height
Answer:
3 cm
Step-by-step explanation:
Given dimensions of the cuboid:
Length (l) = 10 cmWidth (w) = 2 cmHeight (h) = x cmIf the total surface area of the cuboid is 112 cm²:
[tex]\begin{aligned}\textsf{Total SA of cuboid}&= 2 (\sf lh +wh + lw)\\\implies 112&=2(10x+2x+10 \cdot 2)\\112&=2(12x+20)\\112&=24x+40\\24x&=72\\x&=3\end{aligned}[/tex]
Therefore, the height of the cuboid is 3 cm.
What do the Zero Exporient and Negative Exponent Properties mean?
Answer:
Step-by-step explanation:
Zero exponent numbers = 1
When you try to multiply an exponent by zero, it equals one.
Negative exponents is just a 1/x
Negative just flips over the equation.
For example, 9^-1
1/9^1
1/9
Answer:
Step-by-step explanation:
Zero Exponent Property: The zero exponent rule states that when a nonzero number is raised to the power of zero, it equals 1.
Example: x^0 = 1
Negative Exponent Properties: the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice verse. It also describes how many times we have to multiply the reciprocal of the base.
An example of negative exponents is [tex]3^{-2}[/tex].
Samir and Elizabeth deposit $600.00 into a savings account which earns 1% interestcompounded quarterly. They want to use the money in the account to go on a trip in 2 years.How much will they be able to spend?nt)"Use the formula A = P 1 + , where A is the balance (final amount), P is the principal(starting amount), r is the interest rate expressed as a decimal, n is the number of times peryear that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.$
To determine a compound Interest
The above formular is for solving compound interest
[tex]\begin{gathered} P\text{ = Principal = \$600, A = Amount , r = rate = 1 \% = 0.01 } \\ n\text{ = number of times quartely = }\frac{12}{4}=3\text{ , t = time in years = 2} \end{gathered}[/tex][tex]\begin{gathered} A\text{ = P ( 1 + }\frac{r}{n})^{nt} \\ A\text{ = \$ 600 ( 1 + }\frac{0.01}{3})^{3x2} \\ A=600(1+0.003)^6 \end{gathered}[/tex][tex]\begin{gathered} A=600(1.003)^6 \\ A\text{ = 600(1.020167)} \\ A\text{ = 612.1}002 \\ A\text{ = 612.10 (nearest cent)} \end{gathered}[/tex]Hence the compound interest = 612.10 (nearest cent)
Ming had 59 birthday cupcakes. He gave 30 cupcakes to his classmates at school. Ming's family ate another 11 cupcakes at home.
How many cupcakes does Ming have left?
Answer:18
Step-by-step explanation:
59 - 30 - 11 = 18
Part III: Verify that
f(g(x)) = F(x)
f(g(x)) = √3x - 4
(2 points)
they seem to be right :p
Step-by-step explanation:
Pls help if able to send a picture of answer and work
Joan walked 20 brown dogs.
As per the question, the 40% of total number of dogs are brown. So, finding 40% of the number 50 will give us the number of brown dogs.
Number of brown dogs = 50×40%
Converting Percentage to fraction
Number of brown dogs = 50×40/100
Cancelling zero as it is common
Number of brown dogs = 5×4
Performing multiplication to find the number of brown dogs
Number of brown dogs = 20
Thus, out of 50 dogs, Joan walked 20 brown dogs.
Learn more about Percentage -
https://brainly.com/question/24304697
#SPJ1
What is 2/5 divided by 1/10?
Answer:
4
Step-by-step explanation:
2/5 divided by 1/10
Division of fractions
Use copy dot flip
2/5 * 10/1
20/5
4
What is the value of x in the equation −x = 6 − 3x + 8?−14−7147
S={7}
1) Let's solve for x, for the given equation :
-x = 6 -3x +8 Add 3x to both sides
3x-x=-3x+3x +6 +8
2x =14 Divide both sides by 2
x= 7
S={7}
And that is the answer
How many terms are in this expression?
9c + a
Answer:
2
9c and a
Step-by-step explanation:
Answer:
2, (a and c)
Step-by-step explanation:
what is 3/4+65/8-23+78+92-6+g
Answer:
g + 1199 / 8
Step-by-step explanation:
3/4+65/8-23+78+92-6+g
1199/8+g
What are the y-intercept and the horizontal asymptote of g(x) = 7x + 2?
(0, 3) ; y = 2
(0, 4) ; y = 7
(0, 7) ; y = 2
(0, 9) ; y = 7
The y-intercept and the horizontal asymptote of g(x) = 7ˣ + 2 is (a) (0, 3) ; y = 2
How to determine the y-intercept?The equation of the function is given as
g(x) = 7ˣ + 2
To calculate the y-intercept, we set x = 0
So, we have
g(0) = 7⁰ + 2
Evaluate the exponent
g(0) = 1 + 2
Evaluate the sum
g(0) = 3
So, we have
(x, y) = (0, 3)
How to determine the horizontal asymptote?The equation of the function is given as
g(x) = 7ˣ + 2
To calculate the horizontal asymptote, we set 7ˣ
So, we have
y = 0 + 2
Evaluate the sum
y = 2
Hence, the solution is (a) (0, 3) ; y = 2
Read more about y-intercept at
https://brainly.com/question/15709421
#SPJ1
The required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.
What is an asymptote?Asymptote is the line on the curve that does not intersect the curve but passes as near to the maximum and minimum of the graph.
Here,
The y-intercept of the given function is evaluated as put the x coordinate to zero,
So,
g(0) = 1 + 2
g(0) = 3
Now, the horizontal asymptote is a line that passes near to the line but does not intersect with the curve,
So,
Terminating the x compositon of the function 7ˣ = 0 the rest will be the horizontal asymptote,
y = 7ˣ + 2
y = 0 + 2
y = 2
Thus, the required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.
learn more about asymptote here:
https://brainly.com/question/4084552
#SPJ1
12. Find m<1 and m<2 for a//t
0
please help
Answer:
Angle 1 & 2 are both 100 degrees
Step-by-step explanation:
In the picture,
angles on the same side of the line must add up to 180degrees.
Angles directly opposite of each other(same vertices) must be equal.
with parallel lines, angles that are made by the same intersecting line are also equal.
image really helps :( sry its hard to explain in words
Does anyone know the answers to this problem?
The cups of sugar needed is 2.5 cups.
The cups of flour needed is 3.75 cups
The cups of butter needed is 1.25 cups.
How much sugar, flour and butter is needed?Given the information in the question, the ratio of sugar to flour to butter is 1 : 1.5 : 0.5
Cups of sugar needed = (ratio representing sugar / sum of ratios) x total number of cups
Sum of ratios = 1 + 1.5 + 0.5 = 3
Cups of sugar needed = (1 / 3) x 7.5 = 2.5 cups
Cups of flour needed = (ratio representing flour / sum of ratios) x total number of cups
Cups of flour needed = (1.5 / 3) x 7.5 = 3.75 cups
Cups of butter needed = (ratio representing butter / sum of ratios) x total number of cups
Cups of butter needed = (0.5 / 3) x 7.5 = 1.25 cups
To learn more about ratios, please check: https://brainly.com/question/19910662
#SPJ1
2b+3=7
2z+2=8
6b+2=14
7d−3=18
Answer:
b=2
z=3
again b=2
d=3
Step-by-step explanation:
don't know what to explain