Answer:
The equation of the line is 5x + y + 19 = 0
Step-by-step explanation:
The equation of the line with slope 'm' and given a point (x₁, y₁) passing through it we use the Slope - one - point form which is given by:
y - y₁ = m(x - x₁)
The point given is: (-3, -4) and the slope is -5.
We get the equation of the line to be:
y - (-4) = -5(x - (-3))
⇒ y + 4 = -5(x + 3)
⇒ y + 4 = -5x - 15
⇒ 5x + y + 19 = 0. is the required equation of the line.
Which is the quotient of 3.12÷6.5 a 0.0 48B 0.48C 4.8 D 48
Answer:
B
Step-by-step explanation:
Quotient means divide. I just used a calculator to divide it.
On a very cold morning,it was -7%f.As the day went on,the temperature rose 3 degrees each hour.Which equation shows the temperature over time?
Answer:
The equation that shows the temperature over time is t(x) = -7 + 3x
Step-by-step explanation:
Given:
Temperature at every morning = -7°F
Rise in Temperature per hour = 3 degrees
To Find:
Equation that shows the temperature over time
Solution:
Let x be the time (hours)
Now the temperature at time x (hours) is
=> [tex]-7 + (\text{Number of hours} \times \text {Increase in temperature per hour)}}[/tex]
=>-7 + 3x
Hence at time x hours the temperature will be
t(x) = -7 + 3x
This table gives a few (z,y) pairs of a line in the coordinate plane.
-56 66
-42 58
-28 50
What is the y-intercept of the line?
Answer:
The y-intercept of the line is 34.
Step-by-step explanation:
There are few points on the z-y plane through which a straight line passes.
The points are (-56,66), (-42,58) and (-28,50).
Now, take the first two points to get the equation of the straight line.
The equation is [tex]\frac{y - 58}{58 - 66} = \frac{z - (-42)}{-42 - (- 56)}[/tex]
⇒ [tex]\frac{y - 58}{- 8} = \frac{z + 42}{14}[/tex]
⇒ 14(y - 58) = - 8(z + 42)
⇒ [tex]y - 58 = - \frac{8}{14}z - 24[/tex]
⇒ [tex]y = - \frac{8}{14}z + 34[/tex]
This equation is in slope-intercept form.
Hence, the y-intercept of the line is 34. (Answer)
Help asap, can't figure this out.
Answer:
B. 70
Step-by-step explanation:
[tex]7 \div 12 = \frac{7}{12} \\ 120 \times \frac{7}{12} = 70[/tex]
Answer:
B
Step-by-step explanation:
Given that for every 12 seeds, 7 grew into plants
Then for 120 seeds, that is 120 ÷ 12 = 10 times as many seeds, thus
number growing into plants = 10 × 7 = 70 → B
Question 1 of 5
2 Points
What is the simplified fractional equivalent of the terminating decimal 0.25?
O
O A.
CINNICT
O
O c. 1
O D. 25
SUBMIT
Answer:
The simplified fractional equivalent is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
we know that
A terminating decimal is a decimal that ends. So, it's a decimal with a finite number of digits.
we have
[tex]0.25[/tex]
Let
[tex]x=0.25[/tex]
Multiply by 100 both sides
[tex]100x=25[/tex]
Divide by 100 both sides
[tex]x=\frac{25}{100}[/tex]
Simplify
Divide by 25 both numerator and denominator
[tex]x=\frac{1}{4}[/tex]
Unit Test Review
Active
Yellow light has a frequency of 5.2 x 1014 Hz and travels at a speed of 3.0 x 108 m/s. What is the wavelength of yellow light, in
meters?
5.8 x 10-7m
2.2 x 10-6m
1.7 106 m
8.2 * 1022 m
Save and Exit
Next
Submit
the
the answer is 5.8 x 10-7m
your welcome
The required wavelength of the yellow light is [tex]5.8\times10^{-7}[/tex] m
The correct option is (A).
Wavelength:
The wavelength can be calculated when frequency and speed of the wave are given as
wavelength [tex]\lambda[/tex] = [tex]\frac{v}{f}[/tex]
where v is the velocity of the wave and f be the frequency of the wave.
How to calculate wavelength?Here we have given that
The frequency f = [tex]5.2 \times10^{14}[/tex] Hz
The speed v = [tex]3 \times10^{8}[/tex] m/s
Therefore substitute into above formula
Wavelength [tex]\lambda[/tex]= [tex]\frac{3\times10^{8}}{5.2\times10^{14}}}[/tex]
Wavelength [tex]\lambda[/tex] = [tex]\frac{3}{5.2}\times10^{8-14}[/tex]
Wavelength [tex]\lambda[/tex] = [tex]0.5769\times10^{-6}[/tex]
Wavelength [tex]\lambda[/tex] = [tex]0.5769\times10^{-6}[/tex]
Wavelength [tex]\lambda[/tex] = [tex]5.769\times10^{-7}[/tex]
Wavelength [tex]\lambda[/tex]= [tex]5.8\times10^{-7}}[/tex] m
Therefore the correct option is (A).
This is the conclusion to the answer
Learn more about wavelength here-
https://brainly.com/question/16749356
#SPJ2
Write an equation in point-slope form for the line that is perpendicular to the given line and passes through the given point.
Y - 3 = 4 (x + 2) through the point ( -2,6
Answer:
y-6=-1/4(x+2)
Step-by-step explanation:
y-3=4(x+2)
y=4x+8+3
y=4x+11
-------------
Perpendicular means negative reciprocal of the slope.
y-6=-1/4(x-(-2))
y-6=-1/4(x+2)
10 POINTS!!
Suppose a snow cone has a paper cone that is 8 centimeters deep and has a diameter of 5 centimeters. The flavored ice comes in a spherical scoop with a diameter of 5 centimeters and rests on top of the cone. If all the ice melts into the cone, will the cone overflow? Explain.
Answer:
D
Step-by-step explanation:
We require to calculate the volume (V) of the cone and sphere.
The volume of a cone is calculated as
V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )
Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus
V = [tex]\frac{1}{3}[/tex]π × 2.5² × 8 ≈ 52.36 cm³
The volume of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius )
Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus
V= [tex]\frac{4}{3}[/tex]π × 2.5³ ≈ 65.45 cm³
Since volume of the sphere is greater than the volume of the cone
Thus when the ice cream melts it will overflow → D
If w=45,what is the value of 2(w-7)
Answer:
76
Step-by-step explanation:
if w=45, you'd get 2(45-7) by replacing the variable (w) with its value (45)
so first you'd distribute 2 to the 45 and the 7
now it'd be:
90-14=76
so the answer would be 76! :)
Answer:
The answer is 76
Step-by-step explanation:
First you swap in the number like so: 2(45-7)
Then you figure out what's is the parentheses first going with PEMDAS like so : 2(38)
Finally you multiply the number getting your final answer which is :76
Si n es un número impar,¿ cual de las siguientes opciones representa un numero par? a) 2n +1 b) n(n+2) c) n+(n-1) e) 2(n+1)
Answer: e) 2(n+1)
Step-by-step explanation:
De las opcionas dadas, e) 2(n+1) es la correcta.
Empecemos por explicar la siguiente regla:
(número par)(número par)=número par
(número par)(número impar)=número par
(número impar)(número impar)=número impar
Ahora bien, en la expresión 2(n+1) el resultado de lo que se encuentra dentro del paréntesis va a ser multiplicado por 2, el cual es un número par, por lo tanto el resultado final va a ser un número par independientemente de si lo que está en el paréntesis es par o impar.
Por ejemplo, si elegimos 1 que es impar:
2(1+1)=2(2)=4
El resultado es par.
Si probamos con las otras opciones, los resultados serán impares:
a) 2n +1
2(1)+1=2+1=3 impar
b) n(n+2)
1(1+2)=1(3)=3 impar
c) n+(n-1)
1+(1-1)=1+0=1 impar
What is the equation of the line in slope-intercept form?
y=_ x +_
Answer:
y = 5/2x + 5
Step-by-step explanation:
Your b value is the place where the line crosses the y-axis. So, we can tell right away the b value in the equation is 5.
I'll use negative 2 as the point to find the slope. You go down 5, so we have -5, and go left 2, so -2. 2 negatives make a positive, so the slope is 5/2.
Final equation -
y = 5/2x + 5
Select the correct answer from each drop down
Answer:
The average rate of change on [1,3] is [tex]\frac{1}{2}[/tex] the average rate of change on [2,4]. The average rate of change on [1,3] is [tex]\frac{2}{5}[/tex] the average rate of change on [1,5]. So the function can not be linear.
Step-by-step explanation:
See the table attached.
The average rate of change on [1,3] is = [tex]\frac{32 - 8}{3 - 1} = 12[/tex]
The average rate of change on [2,4] is = [tex]\frac{64 - 16}{4 - 2} = 24[/tex]
Again, the average rate of change on [1,5] is = [tex]\frac{128 - 8}{5 - 1} = 30[/tex]
Therefore, the average rate of change on [1,3] is [tex]\frac{1}{2}[/tex] the average rate of change on [2,4]. The average rate of change on [1,3] is [tex]\frac{2}{5}[/tex] the average rate of change on [1,5]. So the function can not be linear. (Answer)
A lake near the Arctic Circle is covered by a
22
2
2
-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After
33
3
3
weeks, the sheet is only
1.251.25
1.25
1, point, 25
meters thick.
Let
SS
S
S
represent the ice sheet's thickness (in meters) after
tt
t
t
weeks.
Answer:
S = 2 - 0.25W
Step-by-step explanation:
A lake near the Arctic Circle is covered by a 2 meters thick sheet of ice during the cold winter months.
At the warm air of spring gradually melts the ice thickness gradually.
Therefore, the equation that models the situation is S = 2 - bW ....... (1), where S is the remaining thickness of the ice sheet and W is the number of weeks passed and b is the rate of decrease of ice sheet thickness with respect to the number of weeks.
Now, putting W = 3 weeks and S = 1.25 meters in the equation (1) we get,
1.25 = 2 - 3b
⇒ 3b = 0.75
⇒ b = 0.25 meters per week.
Therefore, the equation (1) becomes S = 2 - 0.25W (Answer)
Slope is 4 and (4,6) is on the line
Answer:
y-6=4(x-4)
Step-by-step explanation:
y-y1=m(x-x1)
y-6=4(x-4)
Which expressions are equivalent to z + (z + 6)z+(z+6)z, plus, left parenthesis, z, plus, 6, right parenthesis?
Answer: [tex]2z^{2} + 14 z +6[/tex] and [tex]2(z^{2} + 7 z +3)[/tex]
Step-by-step explanation:
We have the following expression:
[tex]z+(z+6)z+(z+6)z+(z+6)[/tex]
Let's solve it:
[tex]z+z^{2}+6z+z^{2}+6z+z+6[/tex]
We have this result:
[tex]2z^{2} + 14 z +6[/tex]
However if we apply coomon factor 2, we will have a simplified result:
[tex]2(z^{2} + 7 z +3)[/tex]
Which are equivalent ratios to 7:13?
Answer:
14:26, 21:39, 28:52, 35:65, 42:78, 41:91
Step-by-step explanation:
All of the above are equivalent ratios. These are only a few. More can be found by just simply multiplying 7 by any amount, and 13 by any amount.
Ratios that are equivalent to 7:13 from the given options are 21:39, 28:52, and 14:26. Option A, C, D is correct.
To find equivalent ratios, we need to multiply or divide both terms of the ratio by the same non-zero number. Let's go through the options provided:
21:39 - If we divide both terms by 3, we get 7:13, which means this is an equivalent ratio.72:128 - If we divide both terms by 8, we get 9:16, which is not equivalent to 7:13.28:52 - If we divide both terms by 4, we get 7:13, which means this is an equivalent ratio.14:26 - If we divide both terms by 2, we get 7:13, which means this is an equivalent ratio.36:48 - If we divide both terms by 6, we get 6:8, which simplifies to 3:4. This is not equivalent to 7:13.Therefore, the equivalent ratios are 21:39, 28:52, and 14:26.
Hence, A. C. D is the correct option.
The complete question is:
Which are equivalent ratios to 7:13?
A) 21:39
B) 72:128
C) 28:52
D) 14:26
E) 36:48
a cafeteria worker is wondering how student lunch prices at a high school have changed over time. she researches lunch prices for the years 2000 through 2015 and plots the data in a scatter plot. the best-fit line for the data has the equation y=0.057 x + 1.150, where x is the number of years since 2000 and y is the student lunch price, in dollars.
determine whether each statement below is true ot false based on the question of the line best fit. select true or false for each question.
the student lunch price was generally increasing between 2000 and 2015.
the student lunch price was changed by approximately 5.7 cents a year.
the student price in 2015 was approximately $1.15.
Answer:
True false true
Step-by-step explanation:
TRUE, the student lunch price was generally increasing between 2000 and 2015 as the equation [tex]y=0.057x+1.150[/tex] is a linearly increasing function.
TRUE, the student lunch price was changed by approximately [tex]5.7\rm cents[/tex] a year.
FALSE, the student price in 2015 was approximately $1.15.
The best-fit line for the data has the equation [tex]y=0.057x+1.150[/tex] , where [tex]x[/tex] is the number of years since 2000 and [tex]y[/tex] is the student lunch price, in dollars.
So, it can be seen here from the best-fit line equation that it is a linearly increasing function so, the student lunch price was generally increasing between 2000 and 2015.
Now, differentiating the given best-fit line for the data has the equation [tex]y=0.057x+1.150[/tex] with respect to [tex]x[/tex] to determine the approximated change of the lunch price per year
[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(0.057x+1.150)\\\dfrac{dy}{dx}=\$0.057\\\dfrac{dy}{dx}=5.7\rm cents[/tex]
And, [tex]2015[/tex] is [tex]15[/tex] years from the year [tex]2000[/tex] so, substitute the value of the parameter [tex]x=15[/tex] in the best-fit line equation, we get
[tex]y=0.057\times 15 +1.150\\y=0.855+1.150\\y=2.005[/tex]
So, the lunch price in 2015 was approximately [tex]\$2.005[/tex].
Hence, the first two statements are TRUE while the last statement is FALSE.
Learn more about the best-fit line equation here:
https://brainly.com/question/14279419?referrer=searchResults
7. Nick’s youth group has 20 regular students that attend weekly get togethers. They saved up enough money for each person to go swimming 10 times each with the daily pay plan. After they saved that amount, they found out they can use the early pay plan and save money. They plan to donate their savings to the church since it’s in need of a new sound system. How much money will they be able to donate with the savings from all 20 youth? (Please show all your work for full credit)
WILL GIVE BRILIEST
Answer:
If each youth saves $10 daily, their weekly savings would be $1400. So they donated $1400 to the church.
Step-by-step explanation:
Let the daily pay plan for each youth be $y
Daily pay plan for 20 youth = $20y
Weekly pay plan = 7×20y = $140y
Assuming each youth saves $10 daily
Daily savings for 20 youth = 20×$10= $200
Weekly savings for 20 youth = 7×$200= $1400
If they used the early pay plan ($140y) to go swimming, they saved $1400 which they donated to the church.
Answer:
$375 saved or roughly 33%.
Step-by-step explanation:
With daily plan;
(15)4.00 = 60.00
(25)60.00 = $1,500.00
If the youth group saved up enough for each of them to swim 15 times and 25 students are attending, they originally had $1,500.00 saved for the trip.
With early pay;
(25)45.00 = $1,125.00
1,500.00 - 1,125.00 = $375 saved or roughly 33%.
Hope this helps! And please, do not copy-paste this answer. Write it in your own words, thanks <33
HELP I NEED IT TOMMOROW!! I WILL MARK YOU AS A BRAINLIEST!!!
Is profit negative or positive?
Is bill positive or negative?
Answer:
Profit is positive and bill is negative I believe. I hope this helped!
Answer:
Both ( if I had to choose one I would choose negative)
Step-by-step explanation:
The reason for my answer is because it could teach responsibility and time management. But it can also leave people without a home if not payed on time as well as hungry families.
plz hurry!!!! thank you!!!!
Answer:
∠A ≈ 19.47°
Step-by-step explanation:
As you know , the angle that tangent makes with the radius at the point of tangency is 90°.
∴∠OKA = 90°
As AO = 15 and OK = 5 ,
[tex]sin(A) = \frac{OK}{AO}[/tex]
[tex]sin(A) = \frac{5}{15} [/tex]
[tex]sin(A) = \frac{1}{3} [/tex]
∠A = [tex]sin^{-1} (\frac{1}{3} )[/tex]
∠A ≈ 19.47°
Answer:
[tex]\mathbf{m\angle A = sin^{-1}(\frac{1}{3}) \approx 19.47^{\circ}}[/tex]
Step-by-step explanation:
This question involves some basic knowledge of trigonometric function. The following formula only works for right angled triangles.
[tex]\mathbf{sin(x) = \frac{perpendicular}{hypotenuse}}[/tex]
In ΔAKO,
m∠AKO = 90°
Therefore ΔAKO is a right angled triangle. If we take ∠A into consideration then base will be AK, perpendicular will be OK and hypotenuse will be AO.
AO = 15
OK = 5
[tex]\therefore \mathrm{sin(\angle A) = \frac{OK}{AO} = \frac{5}{15} = \frac{1}{3}}[/tex]
[tex]\mathrm{sin(\angle A)=\frac{1}{3}}[/tex]
[tex]\mathrm{\angle A=sin^{-1}(\frac{1}{3})}[/tex]
To calculate [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] use scientific calculator
value of [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] is approximately equal to 19.47°
Therefore [tex]\mathbf{m\angle A \approx 19.47}[/tex]
(NOTE : When a line passing through center of a circle, is drawn to a tangent at the point of tangency then the angle made between then is 90°
Therefore m∠AKO = 90°)
In a shop, apples cost 27p each and oranges cost 36p each.
Muhammed bought some apples and oranges in the shop. He paid £1.53.
Work out how many apples and how many oranges Muhammed bought.
HELP!
Answer:
The number of apple bought is 3
The number of orange bought is 2
Step-by-step explanation:
Given as :
The price of each apple = 27 p = 27 × 0.01 pound = 0.27 pound
The price of each orange = 36 p = 36 × 0.01 pound = 0.36 pound
The Total money paid for the fruits = 1.53 pounds
Let The Total number of apple bought = a
And The Total number of orange bought = o
Now, According to question
Total money paid for the fruits = Total number of apple bought × price of each apple + Total number of orange bought × price of each orange
Or, 0.27 a + 0.36 o = 1.53 ......A
Here The Total quantity of fruits bought is not given, so apply hit and trial method to calculate total number of each fruit
Let The a = 1 and o = 1
So, 0.27 × 1 + 0.36 × 1 = 1.53
∴ 0.63 ≠ 1.53
Again
Put a = 2 , o = 2
So, 0.27 × 2 + 0.36 × 2 = 1.53
∴ 1.26 ≠ 1.53
Again
Put a = 3 , o = 3
So, 0.27 × 3 + 0.36 × 3 = 1.53
∴ 1.89 ≠ 1.53
Now, Let a = 3 , o = 2
So, 0.27 × 3 + 0.36 × 2 = 1.53
∴ 1.53 = 1.53
so, from hit and trial method , we get the number of apple = a = 3
And he number of orange = o = 2
Hence, The number of apple bought is 3
And The number of orange bought is 2 . Answer
Solve the following system of equations graphically: y=3x+4 and y=-2x-5
Answer:
(x, y) = (-1.8, -1.4)
Step-by-step explanation:
Modern graphing calculators make it trivially simple to solve many problems by graphing. It has become my favorite method.
The graph shows the solution to be (x, y) = (-1.8, -1.4).
___
If you're graphing by hand, it is usually convenient to start with the y-intercepts, then draw the lines with the required slopes. These equations are written in slope-intercept form, making that approach relatively simple.
The first equation has a y-intercept of (0, 4) and a slope of 3. So, another point on the graph will be left 1 and down 3 (as opposed to right 1 and up 3). That point is (-1, 1).
The second equation has a y-intercept of (0, -5) and a slope of -2. So, another point on the graph of that will be left 1 and up 2, to (-1, -3)
ork, and INTERPRET answers for word problems.
Chan Hee bought 3.4 pounds of cheese that
cost $6.95 per pound. How much did he spend
on cheese?'
Answer:
He spend on cheese is $23.63.
Step-by-step explanation:
Given:
Chan Hee bought 3.4 pounds of cheese that cost $6.95 per pound.
Now, to find the amount he spend on cheese.
As given the unit rate:
Cost of per pound of cheese = $6.95.
So, to get the amount Chan Hee spend on buying cheese we multiply the number of pounds of cheese to the cost of per pound of cheese.
[tex]Number\ of\ pounds\ of\ cheese\times cost\ of\ per\ pound\ of\ cheese.[/tex]
[tex]=3.4\ pounds\times \$6.95[/tex]
[tex]=\$23.63.[/tex]
Therefore, he spend on cheese is $23.63.
What is 20 minus 5 as distributive property
Answer:
5(4-1)
Step-by-step explanation:
5(4-1)
20-5
5x4= 20
5x1= 5
Solve the quadratic equation by completing the square.
4x2 + 8x - 7 = 0
A) x =
2±
11
2
B) x =
2±
11
4
C) x = -
2±
11
2
D) x = -
2±
11
4
Answer:
x=(-2+sqrt(11))/2, (-2-sqrt(11))/2.
Step-by-step explanation:
Apply the quadratic formula with a=4, b=8 and c=-7.
Solve 4^(x+2) = 12 for x using the change of base formula log base b of y equals log y over log b.
Answer:
[tex]x \approx -0.208[/tex]
Step-by-step explanation:
By applying logarithms to each side of the equation and some algebraic handling:
[tex]x+2 = \log_{4} 12[/tex]
[tex]x + 2 = \frac{\log_{10} 12}{\log_{10} 4}[/tex]
[tex]x = \frac{\log_{10}12}{\log_{10}4} - 2[/tex]
[tex]x \approx -0.208[/tex]
Final answer:
To solve the equation
[tex]4^{x+2} = 12[/tex]for x, you can use the change of base formula log base b of y equals log y over log b. By following the steps, you should find the solution to be x ≈ -0.086.
Explanation:
To solve the equation
[tex]4^{x+2} = 12[/tex]for x, we can use the change of base formula log base b of y equals log y over log b. Let's solve it step by step:
Take the logarithm of both sides of the equation using any base (let's use base 10 for this example): [tex]log (4^{x+2})[/tex] = log 12Apply the power rule of logarithms: (x+2) * log 4 = log 12Divide both sides by log 4: x+2 = log 12 / log 4Subtract 2 from both sides to isolate x: x = log 12 / log 4 - 2Use a calculator to evaluate the right side of the equation: x ≈ -0.086Therefore, the solution to the equation
[tex]4^{x+2} = 12[/tex]is approximately x = -0.086.
line m passes through the points -2,7 and 4,-5 as shown below.
Answer:
y=-2x
Step-by-step explanation:
Answer:
y+2x=8
Step-by-step explanation:
when you put this in slope intercept form it will equal y=-2x+8 . Parallel lines need to have the same slope
Max is trying to prove to his friend that two reflections, one across the x-axis and another across the y-axis, will not result in a reflection across the line y = x for a pre-image in quadrant II. His friend Josiah is trying to prove that a reflection across the x-axis followed by a reflection across the y-axis will result in a reflection across the line y = x for a pre-image in quadrant II. Which student is correct, and which statements below will help him prove his conjecture? Check all that apply
Max is correct.
Josiah is correct.
If one reflects a figure across the x-axis from quadrant II, the image will end up in quadrant III.
If one reflects a figure across the y-axis from quadrant III, the image will end up in quadrant IV.
A figure that is reflected from quadrant II to quadrant IV will be reflected across the line y = x.
If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) (x, –y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) (–x, y).
Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line should give.
Answer:
Max is correct
If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) ⇒ (x, –y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) ⇒ (–x, y).
Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line should give.
Step-by-step explanation:
The answer above pretty well explains it.
The net result of the two reflections will be that any figure will retain its orientation (CW or CCW order of vertices). It is equivalent to a rotation by 180°. The single reflection across the line y=x will reverse the orientation (CW ⇔ CCW). They cannot be equivalent.
Max is correct in stating that two reflections, one across the x-axis and another across the y-axis, will not result in a reflection across the line y = x for a pre-image in quadrant II. Josiah's conjecture is incorrect. Statements that will help Max prove his conjecture include reflecting a figure across the x-axis and the y-axis, and how the coordinates of the image points change in each reflection.
Explanation:Max is correct. When a figure is reflected across the x-axis, the y-coordinate of each point is negated, resulting in an image in a different quadrant. Therefore, reflecting a figure across the x-axis from quadrant II will place the image in quadrant III. Similarly, when a figure is reflected across the y-axis, the x-coordinate of each point is negated, resulting in an image in a different quadrant. Reflecting a figure across the y-axis from quadrant III will place the image in quadrant IV.
A figure that is reflected from quadrant II to quadrant IV will be reflected across the line y = x. However, reflecting a figure across the x-axis followed by a reflection across the y-axis will result in an image that is reflected across the line y = -x, not y = x. Therefore, Josiah's conjecture is incorrect.
The following statements will help Max prove his conjecture:
If one reflects a figure across the x-axis from quadrant II, the image will end up in quadrant III.If one reflects a figure across the y-axis from quadrant III, the image will end up in quadrant IV.If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) → (x, -y).If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) → (-x, y).Therefore, Max's statements are correct and Josiah's conjecture is incorrect.
Mr. Emory bought 6 pizzas for the math team. The total cost of the order was $58.50. Each pizza cost the same amount. What is the unit cost per pizza of the order?
Answer:
58.50/6= $9.75 unit cost for each pizza
which expressions are equivilant to 3x+3(x+y)
Step-by-step explanation:
3×+3(x+y) is equal to 6x+3y