Suppose line m is the line with the equation x = -5, line n is the line with the equation y = 1, line g is the line with the equation y = x, and line h is the line with the equation
y = -2. given a(9,-3), b(6,4), and c(-1,-5), what are the coordinates of the vertices of aa'b'c' for the reflection rg?
Answers
A' will be (-3,9) B' will be (4,6) and C' will be (-5,-1). t are the coordinates of the vertices of aa'b'c' for the reflection rg.
What is coordinates ?A pair of numbers that specify where a point is situated on a coordinate plane using the horizontal and vertical separations from the two reference axes. usually represented by a pair of x-values and y-values (x,y).
CalculationIn this problem, basically you have three points and 6 straight lines(4 described in the problem and x and y axis) in a 2-D plane. You have to find the reflection of these three points with respect to these 6 lines one by one.
Points are:
A(9,-3)
B(6,4)
C(-1,-5)
Case 1:
Line is X-axis i.e. y = 0.
If you take reflection about x-axis then you can observe that the x - co-ordinate will remain same while y-co-ordinate will change its sign.
So A' will be (9,3), B' will be (6,-4) and C' will be (-1,5)
Case 2:
Line is y-axis i.e. x = 0
Here the analogy will remain same except here the y - co-ordinate will remain same and x - co-ordinate will change ite sign.
So, A' will be (-9,-3) B' will be (-6,4) and C' will be (1,-5).
Case 3:
Reflection about line "m" i.e. x = -5
This is a vertical line. Suppose the point whose reflection is to be found about is line is at a perpendicular distance of "k" from the line on right side, then its reflection will be "k" distance on the left from this line on the same horizontal line. So y-co-ordinate will not change.
For A(9,-3), it is at a distance of 14 units from the line on the right side so its reflection will be 14 units on the left with same y - co-ordinate. So its x - co-ordinate will be -5-14 = -19
So A' will be (-19,-3)
Similarly for B, B' will be (-16,4) and C' will be (-9,-5).
This graph will help you understand better.
The red line is x = -5.
The case for line y = 1 and y = -2 will be similar.
Case 5:
Reflection about the line y = x
photos are attached .............
So, A' will be (-3,9) B' will be (4,6) and C' will be (-5,-1).
We can use these two observations to find the reflection of any point about any line:
(i) The midpoint of the given point and the reflection point will lie on the given line about which the reflection is to be found.
(ii) The product of slope of given line and the line joining the given point and the reflection point is -1.
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Related Questions
A ferry travelled from Jetty A to Jetty B in 3 h. It then travelled from Jetty B back to
Jetty A in 2 h. The distance between the two jetties was 80 km.
Find the total time taken for the whole journey.
Find the average speed for the whole journey.
Answers
Average Speed = 160÷5= 32km/hr
Given,
A ferry traveled from Jetty A to Jetty B in 3 h. It then traveled from Jetty B back to Jetty A in 2 h. The distance between the two jetties was 80 km.
To find,
Total time for the whole journey,
Solution: Time is taken from Jetty A to Jetty B = 3 hours
and Jetty B to Jetty A = 2 hours
Total time = 3 h + 2 h = 5 h
Average Speed = Total Distance ÷ Total Time
Since, Total distance = 80×2= 160
Average Speed = 160÷5= 32km/hr
a) 5 hours
b) 32km/hr
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3. In the figure below, XU is the midsegment of TVW and is parallel to VW, determine the length of XU. (3 points) 11x + 2 U 10x + 16
Answers
If XU is the midsegment of TVW, then, it is necessary that:
(11x + 2)/(10x + 16) = 1/2
multiply the previous equation by 10x + 16:
11x + 2 = 1/2(10x + 16)
11x + 2 = 5x + 8 subtract 5x and 2 both sides
11x - 5x = 8 - 2
6x = 6
x = 6/6
x = 1
THe length of XU is:
XU = 11x + 2 = 11(1) + 2
XU = 13
1. A contractor is building a new room onto the back of
Darnell's house. The contractor adds a diagonal brace to
the frame of one of the walls. The frame is 15 feet long
and 8 feet tall. How long is the diagonal brace?
Answers
Answer:
the answer is 23
Step-by-step explanation: use the formala of a triangle
which means you either add or subtract the sides and since it is the big side you are missing you have to add and when you do you get 23
A toy rocket was fired into the air. The height, h,of the rocket at time t seconds is recorded in the tablebelow. Using an equation to model the data, find theheight of the rocket after 5 seconds.
Answers
we have the ordered pairs
(0,0)
(1,76)
(2,120)
(3,132)
(4,112)
Plot the given points
see the attached figure
In this problem we have a vertical parabola open downward
The vertex represents a maximum
The equation is of the form
y=ax^2+bx+c -----> quadratic equation
using a quadratic regression calculator
we have that
a=-16
b=92
c=0
therefore
y=-16x^2+92x
For x=5 sec
substitute
y=-16(5)^2+92(5)
y=60
the answer is
the height is 60 unitsAlternative method (approximate solution)
The quadratic equation in vertex form is equal to
y=a(x-h)^2+k
where
(h,k) is the vertex
I will assume that the vertex in this problem is the point (3,132)
so
(h,k)=(3,132)
substitute
y=a(x-3)^2+132
Find out the value of a
we have the point (0,0)
substitute in the equation
0=a(0-3)^2+132
0=9a+132
a=-132/9
a=-14.67
therefore
y=-14.67(x-3)^2+132
For x=5
y=-14.67(5-3)^2+132
y=73.33 units
Third Method
using the equation
y=ax^2+bx+c
points (0,0), (1,76) and (2,120)
(0,0) --------> 0=a(0)^2+b(0)+c ----------> c=0
y=ax^2+bx
(1.76) ------> 76=a(1)^2+b(1) ----------> a+b=76 ------> equation 1
(2,120) ----> 120=a(2)^2+b(2) ----> 4a+2b=120 ----> equation 2
solve the system of equations
the solution of this system is
a=-16
b=92
therefore
the equation is
y=-16x^2+92x (same first method)graph the linear function identify the x-intercept.
y=-x
Answers
The x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.
What is the x-intercept?A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = MX + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.So, plot the linear function:
Plot y = -x as follows:(Refer to the graph attached below)
We can clearly see that the x-intercept is 0.Therefore, the x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.
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6. A sandwich store charges a $10 delivery fee, and $4.50 for each sandwich.
a. What is the total cost (sandwiches and delivery charge) if an office orders 6
sandwich?
Answers
Answer:
Step-by-step explanation:
4.50 per sandwich
6 sandwiches
4.50 x 6 = 27
+ Delivery fee $10
$27 + $10 =
$37 total
find area and perimeter
Answers
Answer:
Area: 20cm^2
perimeter: 20cm
(4*2) + (4*3) =
8 + 12 = 20cm^2
A football is kicked into the air from an initial height of 4 feet. The height, in feet, of the football above the ground, is given by s(t) = -16t^2 + 50t + 4, where the t is time, in seconds, and t>= 0. At what time will the football be 25 feet above the ground?
Answers
The time at which the football is 25 feet above the ground is 1/2 seconds and 21/8 seconds.
Given that:-
[tex]s(t) = -16t^2 + 50t + 4[/tex]
Where s(t) represents the distance traveled by the football after t seconds.
We have to find the time at which the football is 25 feet above the ground.
Putting s (t) = 25 feet, we get,
[tex]25 = -16t^2 + 50t + 4\\\\ -16t^2 + 50t -21=0\\\\ 16t^2 - 50t - 21=0[/tex]
Using middle term split theorem to solve the equation, we get,
[tex]16t^2 -42t -8t+ 21=0[/tex]
2t(8t - 21) -(8t-21) = 0
(8t - 21)(2t - 1) = 0
t = 21/8 and 1/2 seconds.
Hence, the time at which the football is 25 feet above the ground is 1/2 seconds and 21/8 seconds.
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Solve for x. Enter the solutions from least to greatest.
(x-7)²-25= 0
lesser =
greater x =
Answers
The values for the lesser and greatest are:
-14 and 0
Step 1: Define
(x + 7)² - 49 = 0
Step 2: Solve for x
Add 49 to both sides: (x + 7)² = 49
Square root both sides: x + 7 = ±7
Subtract 7 on both sides: x = -7 ± 7
Evaluate: x = -14, 0
Step 3: Check
Plug in x values into original equation to verify they are a solution.
x = -14
Substitute in x: (-14 + 7)² - 49 = 0
Add: (-7)² - 49 = 0
Exponents: 49 - 49 = 0
Subtract: 0 = 0
Here we see that 0 does indeed equal 0.
∴ x = -14 is a solution of the equation
x = 0
Substitute in x: (0 + 7)² - 49 = 0
Add: 7² - 49 = 0
Exponents: 49 - 49 = 0
Subtract: 0 = 0
Here we see that 0 does indeed equal 0.
∴ x = 0 is also a solution of the equation.
Hence we get the required answer.
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What would the monthly payment be on a $9,000 car loan at 8.85% interest for a five-year term?
Answers
Answer:
186.17
Step-by-step explanation:
Clarissa had 72 candy bars to sell. She sold 4 per day for 8 days. She ordered 15 more candy bars to share with her 3 friends. The following expression can be used to find the number of candy bars Clarissa had left.
(I need the answer ASAP please!
72 – 4 • 8 – 15 ÷ 3
Based on this expression, how many candy bars did Clarissa have left?
Answers
The number of candy bars Clarissa had left are 55
Given,
In the question:
Clarissa had 72 candy bars to sell. She sold 4 per day for 8 days. She ordered 15 more candy bars to share with her 3 friends.
To find the number of candy bars Clarissa had left.
Now, According to the question:
Total candy sells is 72
Sold candy = 4 per day for 8 days
Sharing candy is 15
Based on the given conditions,
Formulate:
15 + 72 - 8 x 4
Calculate the product or quotient:
15 + 72 - 32
calculate the sum or difference
87 - 32
= 55
Hence, the number of candy bars Clarissa had left are 55.
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Answer: 35
Step-by-step explanation:
Im doing a practice assignment and im not the best at word problems Im not understanding the question
Answers
A sample statistic is is any quantity from the sample of a population.
We can see in the last option, that from the population (total of subjects of study) Kaisa, selected 84 of the total students. This fits in to the definition of sample statistic.
Thus, the correct option is the last one.
what is minus sixteen minus minus twenty
Answers
Answer: (-16)-(-20)= 4
Step-by-step explanation:
the lengths of the upper end lower bases of a trapezoid are 6 centimeters and 10 centimeters respectively, and the distance between them is 15 centimeters. what is the area of the trapezoid
Answers
Given data:
The upper end length of the trapezoid is: a=6 cm
The lower end length of the trapezoid is: b=10 cm
The height of the trapezoid is: h=15 cm
The expression to calculate the area of the trapezoid is,
[tex]A=\frac{1}{2}\times h\times(a+b)[/tex]Substitute vall known values in the above expression.
[tex]\begin{gathered} A=\frac{1}{2}\times15\times(6+10) \\ =\frac{1}{2}\times15\times16 \\ =\frac{240}{2} \\ =120cm^2 \end{gathered}[/tex]Thus, the area of the trapizoid is 120 square centi meter.
10. What is the equation of the directrix for the parabola-8(y - 3)=(x +4)2?A) y=5B) y=1C) y=-2D) y=-6
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
The equation of the directrix for the parabola:
[tex]-8\text{ \lparen y-3\rparen= \lparen x+ 4\rparen}^2[/tex]Step 2:
The details of the solution are as follows:
Next, we can see that the equation of the directrix for the parabola is at:
[tex]\text{y = 5 }[/tex]This is because:
[tex]\begin{gathered} y\text{ -3 = \lparen}\frac{-1}{8})\text{ \lparen x + 4 \rparen}^2 \\ y\text{ = \lparen-}\frac{1}{8})\text{ \lparen x + 4\rparen}^2+\text{ 3} \end{gathered}[/tex]Then, y = k - p
y = 3 - p
p = 1/ 4a
p = 1 / 4(-1/8)
p = -2
y = 5
The following is a pie chart that presents the percentages spent by a certain household on its five largestannual expenditures. What percentage of the money was spent on housing, insurance, and utilities?Choose one. 5 pointsHOUSING 24.8% , FOOD 27.7%, insurance 26.7%, recreation 7.9% UTILITIES 12.9
Answers
1) Since in this pie chart, we have a budget. Let's locate the sectors for Housing, Insurance, and utilities
2) Enlisting them:
Housing: 24.8%
Insurance: 26.7%
Utilities: 12.9%
\%
So we can add them up:
[tex]undefined[/tex]A Saint Bernard puppy weighs 21 1/2pounds at nine weeks old. After that, it gains 2/5 pounds perweek on average. How many weeks old must the puppy be if it weighs 25 1/10 pounds
Answers
From the information available, the puppy weighs 21 1/2 pounds (or 21.5 pounds) at nine weeks old. We shall take this to be the initial value. Hence, we can deduce the following function that relates the weight to the age (in weeks).
[tex]f(x)=21\frac{1}{2}[/tex]However,the puppy gains weight at the rate of 2/5 pounds per week.
Using the weight at nine weeks as the initial value as shown above, we would now have the function re-written as;
[tex]f(x)=21\frac{1}{2}+\frac{2}{5}x[/tex]However, the weight currently is given as 25 1/10 pounds, and we can insert this into the output of the function and then derive the input, as follows;
[tex]undefined[/tex]i need help i suck at dividing decimal
Answers
453.6 divided by 8.1 answer: 56
264.684 divided by 4.2 answer: 15.004
Answer: 1. 0.185185185 keeps going
2. 56
3. 63.02
Step-by-step explanation:
what is this help me i need fast help
Answers
The solution for the equations are :
She subtracts 12 from w , divides by 3 , then multiplies by 6 = 2w - 24
She subtracts 12 from w , multiplies by 3 , then divides by 6 = w/2 - 6
She multiplies w by 3 , subtracts 12 , then divides by 6 = w/2 - 2
She divides w by 3 , subtracts 12 , then multiplies by 6 = 2w - 72
She multiplies w by 6 , subtracts 12 , then divides by 3 = 2w - 4
She divides w by 6 , subtracts 12 , then multiplies by 3 = w/2 - 36
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Winnie is thinking of a number = w
Now ,
a)
She subtracts 12 from w , divides by 3 , then multiplies by 6
So , the equation will be
A = ( (w - 12 ) / 3 ) x 6
A = ( w - 12 ) x 2
A = 2w - 24
Therefore , the equation is 2w - 24
b)
She subtracts 12 from w , multiplies by 3 , then divides by 6
So , the equation will be
A = ( ( w - 12 ) x 3 ) / 6
A = ( w - 12 ) / 2
A = w/2 - 6
Therefore , the equation is w/2 - 6
c)
She multiplies w by 3 , subtracts 12 , then divides by 6
So , the equation will be
A = ( 3w - 12 ) / 6
A = w/2 - 2
Therefore , the equation is w/2 - 2
d)
She divides w by 3 , subtracts 12 , then multiplies by 6
So , the equation will be
A = ( ( w/3 - 12 ) ) x 6
A = ( w/3 ) x 6 - 12 x 6
A = 2w - 72
Therefore , the equation is 2w - 72
e)
She multiplies w by 6 , subtracts 12 , then divides by 3
So , the equation will be
A = ( 6w - 12 ) / 3
A = ( 6w ) / 3 - 12/3
A = 2w - 4
Therefore , the equation is 2w - 4
f)
She divides w by 6 , subtracts 12 , then multiplies by 3
So , the equation will be
A = ( w/6 - 12 ) x 3
A = ( w/6 ) x 3 - 12 x 3
A = w/2 - 36
Therefore , the equation is w/2 - 36
Hence , the equations are evaluated and solved
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Which answer choice uses exponents to show the expression below?
10(5 · 5 + 10) − 2 · 2 · 2
Answers
Answer:
5² · 10 + 10² - 2³
Step-by-step explanation:
10(5 · 5 + 10) − 2 · 2 · 2 =
= 5² · 10 + 10² - 2³
if X-2₁ X-3 and X+4 are factors of f(x)=x³ +ax² + bx+c then what are the possible Values of ab and c?
Answers
The values of a, b, c are a = -1, b = -14, c = 24
Given expression is f(x)=x³ +ax² + bx+c,
To find out the values of a, b, c:
There are two methods
Method - 1:
(x-2)(x-3)(x+4)= x³ +ax² + bx+c
Now we have to compare coefficients as
a = -1, b = -14, c = -24
Method - 2:
If (x-2) is a factor, then x = 2 is a solution. If x = 2 is a solution, then if we substitute x = 2, the polynomial will equal 0.
The same with x-3 and x+4. We can form 3 equations which we can solve simultaneously.
So, Equation 1 = 8+4a+2b+c = 0
Equation 2 = 27+9a+3b+c = 0
Equation 3 = -64+16a-4b+c = 0
As you can see, we get the same answer, just with a different methods.
Hence the answer is, the values are a = -1, b = -14, c = 24.
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Determine if the expression -b^{3}c−b 3 c is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answers
The expression -b³c is the polynomial. The type of the polynomial is cubic polynomial and the degree is 3.
Polynomial:
Polynomial is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Given,
Here we have the expression -b³c.
And we need to find the following:
1) check it if is polynomial or not
2) type of the polynomial
3) degree.
As per the given definition, the expression -b³c is the polynomial.
Here we have the expression -b³c the highest power value for this polynomial is 3.
Therefore, the degree of this polynomial is 3 and the type of the is cubic polynomial.
Because we have identify the type based on the degree value here the value of degree is 3 so the type of the polynomial is cubic one.
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On a floor plan, Bella's rectangular basement measures 3 centimeters by 5 centimeters If the floor plan has a scale of 1 centimeter = 2 meters what is the actual area of Bella's basement?
Answers
Answer:
60 meters^2
Step-by-step explanation:
1/2= 3/x
2(3)=x
6=x
1/2=5/x
x=2(5)
x=10
And then we multiply the 2 sides together
10x6
60
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what 6y=3x-9, in the simplest form
Answers
Answer: x=2y+3
Step-by-step explanation:
Switch around the 6y
3x-9=6y
Add 9 to both sides
3x-9+9=6y+9
3x=6y+9
Divide everything by 3
x=2y+3
Find the equation of the linear function represented by the table below in slope-intercept form.
Answers
Answer:
y= 6x-8
Step-by-step explanation:
you pick two y values and subtract them. then take two x values and subtract them. divide those two awnsers with y on top. the -8 is the y intercept because when x is 0, the y is -8.
Answer:
Step-by-step explanation:
recall slope m is:
slope = m
m = (y2-y1) / (x2-x1)
point P1 (0,-8) in the form (x1,y1)
point P2(1,-2) in the form (x2,y2)
m = { -2-(-8) } / { 1-0 }
m = { -2+8 } / 1
m = 6 /1
m = 6
then plug in any point, I'll use P1
y - y1 = m(x -x1) (point-slope formula)
y - (-8) = 6*(x-0)
y+8 = 6x
y= 6x -8 (slope-intercept formula) :)
A rock is thrown vertically from the ground with a velocity of 28 meters per second, and it reaches a height of -5.2t2 + 28.6t + 4 after t seconds. How many seconds after the rock is thrown will it reach maximum height?
Answers
After 2.75 seconds of motion in the upward direction, the stone will reach maximum height.
What is the general equation of a parabola?The general equation of a parabola is given by y = a(x – h)² + k or
x = a(y – k)² + h. Here (h, k) denotes the vertex
We have a rock which is thrown vertically from the ground with a velocity of 28 meters per second, and it reaches a height of -5.2t² + 28.6t + 4 after t seconds.
We have -
y = - 5.2t² + 28.6t + 4
dy/dx = - 10.4t + 28.6
For maximum height -
dy/dx = 0
- 10.4t + 28.6 = 0
28.6 = 10.4t
t = 28.6/10.4
t = 2.75 seconds
Therefore, after 2.75 seconds of motion in the upward direction, the stone will reach maximum height.
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Janelle plays on her community basketball team, the Raging Rabbits. During their big game against the Porcupines, the Rabbits score 35 points in the first half. They add to their score in the second half. In all, the Rabbits score 90 points. Use an equation for to find the number of points the Rabbits score in the second half.
Answers
Answer:
90-35=x 90-35=55
Step-by-step explanation:
To find your value of X, subtract your score of the first half from your total score.
I'm having some problems with this logarithmic question I will upload a photo
Answers
The Solution.
[tex]Let\log _{\frac{1}{9}}(\frac{1}{9})=x[/tex]Writing the above equation in index form, we have
[tex]\begin{gathered} (\frac{1}{9})^1=(\frac{1}{9})^x \\ Then\text{ it follows that} \\ 1=x \\ x=1 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _749=x \\ So\text{ we have} \\ 49=7^x \\ \text{Making the base of both sides equal, we have} \\ 7^2=7^x \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _{\frac{1}{4}}16=x \\ \\ 16=(\frac{1}{4})^x \\ 16=4^{-1\times x} \\ 4^2=4^{-x} \\ -x=2 \\ x=-2 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _{125}5=x \\ \text{cross multiplying, we have} \\ 5=125^x \\ 5^1=5^{3x} \\ 3x=1 \\ \text{Dividing both sides by 3, we get} \\ x=\frac{1}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _8(\frac{1}{8})=x \\ \\ \frac{1}{8}=8^x \\ \\ 8^{-1}=8^x \\ -1=x \\ x=-1 \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _9(1)=x \\ 1=9^x \\ 9^0=9^x \\ x=0 \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _{\frac{1}{9}}(-1)=x \\ \\ -1=(\frac{1}{9})^x \\ \\ No\text{ solution because it has no real value.} \end{gathered}[/tex](04.02 MC) The table below shows the number of cookies in different numbers of packs: Number of Packs Number of Cookies 2 6 3 9 4 12 5 25 Is this true or false? The numbers in the table represent a proportional relationship. O True O False
Answers
According to the given table, the y-values are triple than x-values except by the last pair (5,25), this means the table does not represents a proportional relationship because the last pair doesn't follow.
Hence, the answer is False.
I need help with this problem. the answer i got was that there is no solution. is that correct?
Answers
Explanation:
To solve the equations by Elimination we can multiply the first equation by -2.5 as follows:
[tex]\begin{gathered} (2x+8y=6)\cdot(-2.5) \\ -2.5\cdot2x-2.5\cdot8y=-2.5\cdot6 \\ -5x-20y=-15 \end{gathered}[/tex]Now, we can add this equation to the second equation as follows:
- 5x - 20y = - 15
5x + 20y = 15
0 + 0 = 0
0 = 0
When we get 0=0, the system has infinite solutions
So, this system has solutions with the form:
(x, y) where 2x + 8y = 6
It also means that both equations, 2x + 8y = 6 and 5x + 20y = 15 are equivalent equations and the solutions of the first one are also the solutions of the second one.