Answers
Answer:
B. 3
Step-by-step explanation:
First of all we will define rotational symmetry.
Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.
The order of rotational symmetry is how many times it matches the original shape during the rotation.
So, for the given shape the rotated shape will match the original shape three times so the order for symmetry for the given shape is 3.
Hence,
the correct answer is B. 3 ..
Related Questions
City a and city b had two different temperatures on a particular day four times the temperature of city a was 8c more than 3 times the temperature of city b the temperature of city a minus twice the temperature of city b was -3c what was the temperature of city a and city b on that day
Answers
Answer:
temperature of city a=5
temperature of city b=4
Step-by-step explanation:
Given:
Let temperature of city A= a
temperature of city B=b
As given:
4a=8+3b
a-2b=-3
rearranging 2nd equation we get:
a=-3+2b
substituting above in 1st equation we get:
4(-3+2b)-3b=8
8b - 12 = 3b + 8
8b-3b=12+8
5b = 20
b = 4
Now substituting b=4 in 4a = 8 + 3b , we get
4a = 8 + 3b
4a = 8 + 3(4)
4a = 8 + 12
4a = 20
a = 20/4
a = 5
temperature of city a and city b on that day is 5C and 4C respectively!
Answer:
The temperature of the city a was 5 °C and b was 4 °C.
Step-by-step explanation:
First we have to write the equations based on the description, this is:
[tex]4a=8+3b\\a-2b=-3[/tex]
Now that we have the equations, we can replace the second in the first:
[tex]4(2b-3)=8+3b[/tex]
Now we can find the value of b:
[tex]8b-12=8+3b[/tex]
[tex]8b-3b=8+12[/tex]
[tex]5b=20[/tex]
[tex]b=\frac{20}{5}[/tex]
[tex]b=4\\[/tex]
Now with the value of b and the second equation we can get the value of a:
[tex]a-2(4)=-3[/tex]
[tex]a-8=-3[/tex]
[tex]a=8-3[/tex]
[tex]a=5[/tex]
The temperature of the city a was 5 °C and b was 4 °C.
help me with the work
Answers
Answer:
Option B k > 0
Step-by-step explanation:
we know that
Observing the graph
The slope of the line is positive
The y-intercept is negative
we have
[tex]3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)[/tex]
The slope of the line is equal to
[tex]m=\frac{1}{3}[5k+2][/tex]
Remember that the slope must be positive
so
[tex]5k+2> 0\\ \\k > -\frac{2}{5}[/tex]
The value of k is greater than -2/5
Analyze the y-intercept
[tex](2-\frac{4}{3}k) < 0\\ \\ 2 < \frac{4}{3}k\\ \\1.5 < k\\ \\k > 1.5[/tex]
1.5 is greater than zero
so
the solution for k is the interval ------> (1.5,∞)
therefore
must be true
k > 0
Is the following relation a function?
x y
1 −2
1 −3
2 1
3 −2
Answers
Answer:
It is not a function!
Step-by-step explanation:
It is not a function!
A function can't have two y-values assigned to the same x-value. In this case, you can se that for x=1 we have two y-values, which are y= -2 and y= -3.
We can have have two x-values assigned to the same y-value, that's why it's okay that for x=1 and x=3 we have the same y-value y=-2
When the polynomial P(x) = 5x3 − 51x2 + kx − 9 is divided by x − 9, the remainder is 0. Which of the following is also a factor of P(x)?
A- x − 5
B- x + 1
C- x − 1
D- 5x + 1
Answers
Answer:
answer C: (x - 1) is also a factor of P(x).
Step-by-step explanation:
Synthetic division is the best approach here. Given that one factor is x - 9, we know that 9 is the appropriate divisor in synthetic division:
9 ) 5 -51 k -9
45 -54 (9k - 486)
----------------------------------
5 -6 (k - 54) (-9 + 9k - 486)
and this remainder must = 0. Find k: -9 + 9k - 486 = 0, or
9k = 486 + 9 = 495
Then k = 495/9 = 55
Look at the last line of synthetic division, above:
5 -6 (k - 54) 0
Substituting 55 for k, we get:
5 -6 1
These are the coefficients of the quotient obtained by
dividing P(x) by (x - 9). They correspond to 5x^2 - 6x + 1.
We must factor this result.
Let's start with 5x + 1, and check whether this is a factor of 5x^2 - 6x + 1 or not. If 5x + 1 is a factor, then the related root is -1/5. Let's use -1/5 as the divisor in synthetic div.:
-1/5 ) 5 -6 1
-1 7/5
----------------------------
5 -7 12/5 Here the remainder is not zero, so -1/5 is
not a root and 5x + 1 is not a factor.
Now try x - 5. Is this a factor of 5x^2 - 6x + 1? Use 5 as divisor in synth. div.:
5 ) 5 -6 1
25 95
------------------------
5 19 96 Same conclusion: x - 5 is not a factor.
Try x = -1:
-1 ) 5 -6 1
-5 11
----------------------
5 -11 12. The remainder is not zero, so (x + 1) is not a factor.
Finally, try x = 1:
1 ) 5 -6 1
5 -1
--------------------
5 -1 0
Finally, we get a zero remainder, and thus we know that x - 1 is a factor of P(x)
Answer C is correct: x - 1 is a factor of P(x)
To solve this question, we can apply the Remainder Theorem. According to the Remainder Theorem, if a polynomial \( P(x) \) is divided by \( x - c \), the remainder of the division is \( P(c) \).
Given:
\( P(x) = 5x^3 − 51x^2 + kx − 9 \)
We are told that when \( P(x) \) is divided by \( x − 9 \), the remainder is 0. Therefore, according to the Remainder Theorem:
\( P(9) = 5(9)^3 − 51(9)^2 + k(9) − 9 = 0 \)
Let's compute \( P(9) \):
\( P(9) = 5(729) − 51(81) + 9k − 9 \)
\( P(9) = 3645 − 4131 + 9k − 9 \)
\( P(9) = 9k − 495 = 0 \)
To solve for \( k \):
\( 9k = 495 \)
\( k = 495 / 9 \)
\( k = 55 \)
Now, we know that P(x) with \( k = 55 \) has no remainder when divided by \( x − 9 \).
The updated polynomial \( P(x) \) is:
\( P(x) = 5x^3 − 51x^2 + 55x − 9 \)
To determine which of the given options is a factor of \( P(x) \), we will test each option by plugging in the roots of these factors into the polynomial \( P(x) \) and checking if it yields zero.
A) For \( x − 5 \), the root is \( x = 5 \):
\( P(5) = 5(5)^3 − 51(5)^2 + 55(5) − 9 \)
\( P(5) = 5(125) − 51(25) + 275 − 9 \)
\( P(5) = 625 − 1275 + 275 − 9 \)
\( P(5) = 625 − 1009 \)
\( P(5) ≠ 0 \) (This factor does not yield zero, so it is not a factor of \( P(x) \).)
B) For \( x + 1 \), the root is \( x = -1 \):
\( P(-1) = 5(-1)^3 − 51(-1)^2 + 55(-1) − 9 \)
\( P(-1) = -5 − 51 − 55 − 9 \)
\( P(-1) = -120 \)
\( P(-1) ≠ 0 \) (This factor does not yield zero, so it is not a factor of \( P(x) \).)
C) For \( x − 1 \), the root is \( x = 1 \):
\( P(1) = 5(1)^3 − 51(1)^2 + 55(1) − 9 \)
\( P(1) = 5 − 51 + 55 − 9 \)
\( P(1) = 60 − 60 \)
\( P(1) = 0 \) (This factor yields zero, so it is a factor of \( P(x) \).)
D) For \( 5x + 1 \), the root is \( x = -1/5 \):
\( P(-1/5) = 5(-1/5)^3 − 51(-1/5)^2 + 55(-1/5) − 9 \)
\( P(-1/5) = -1/25 − 51/25 − 55/5 − 9 \)
Since the coefficients add up to a non-zero value, we can tell that it's not going to be zero; therefore, it is not worth computing the whole expression.
\( P(-1/5) ≠ 0 \) (Hence, this is also not a factor of \( P(x) \).)
The only option that gives a remainder of zero when its root is substituted into \( P(x) \) is C, \( x - 1 \). Therefore, the correct answer is:
C- x − 1
Rate of change questions. How do I answer these 2 questions? (With picture) thanks!
Answers
Question 2
Answer: 1.20
---------
To get this answer, you divide the total amount of royalties (300) over the number of books (250) to get 300/250 = 1.20
Another way to see this is through the ratio of
300 dollars: 250 books
then you divide both parts of that ratio by 250 so that the "250 books" turns into "1 book" like so...
300 dollars: 250 books
300/250 dollars: 250/250 books
1.20 dollars: 1 book
Indicating that his royalties per book is 1.20 dollars. The rate of change is often expressed as a unit rate, meaning that we want the royalties for 1 book (which then scales up).
=========================================================
Question 3
Answer: slope is -1/10 or -0.1; slope tells us how much the candle height is decreasing each minute, y intercept is the starting candle height (see below for further explanation)
---------------
Explanation:
The y intercept is at 25, as this is where the diagonal line crosses the vertical y axis. Similarly, the x intercept is 250. The y and x intercept lead to the two points (0,25) and (250,0). Let's use the slope formula to find the slope of the line through these two points
m = (y2 - y1)/(x2 - x1)
m = (0 - 25)/(250 - 0)
m = -25/250
m = -1/10
m = -0.1
The slope of the line is -1/10 or the decimal equivalent -0.1
What does the slope tell us? It tells us how much of the candle's height is changing as each minute ticks by. Specifically, the slope -0.1 means that the candle height is going down by 0.1 cm for each minute gone by. A shorter way to say this is to say "the height is decreasing by 0.1 cm per minute" (think of it like a speed such as miles per hour)
The y intercept is the starting height of the candle due to the fact that x = 0 here. Therefore, the starting height of the candle is 25 cm.
Side note: the x intercept of 250 tells us how long the candle burns for, which in this case is 250 minutes (4 hrs, 10 min) because y = 0 for the x intercept, and y is the height of the candle at time x. Anything beyond x = 250 is not possible in realistic sense as we can't have a negative y height value.
Please help, willing to give brainleist to whoever helps me:))))) view pic below
Answers
Answer:
A. Drusilla
Step-by-step explanation:
The line of random numbers is used for numbered population.
As we can see that the students are already labelled we have to divide the random number line in pairs of 2 digits
59,78,44,43,12,15,95,40,92,33,00,04,67,43,18,02,61,05,73,96,16,84,33,84,54
We have to keep in mind that our serial numbers are till 29.
So read the pair of numbers one by one
59 can't be used as it is greater than 29. Similarly 78,44,43 cannot be used.
The first student will be: 12 Kiefer
Then 15 and 00 will be second and third.
So the fourth student will be: 04 Drusilla
Hence option A is correct ..
During the geometry unit, Mrs. Hamade asked her class to make kites in the shape of trapezoids. 8 /9 of the class made trapezoid kites. Only 1 /4 of the trapezoid kites could actually fly. What fraction of the classes' kites flew
_____ of the kites flew
Answers
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
THe most common mistake would be to think 1/4th of the kites flew, BUT 1/4th of the trapezoidal kites flew.
Hence, 1/4th of 8/9th of the TOTAL KITES FLEW, that is:
[tex]\frac{1}{4}*\frac{8}{9}=\frac{2}{9}[/tex]
hence, 2/9th of the kites flew
which equation represents a line that passes through (-9,-3) and slope of -6
Answers
Answer:
y + 3 = -6(x + 9) or y = -6x - 57
Step-by-step explanation:
We can use the point-slope form for this situation.
Point-slope form: y - y₁ = m(x - x₁), where m = slope and (x₁, y₁) are given coordinates.
Plug in: y + 3 = -6(x + 9)
This can be changed to the more common slope-intercept form.
Multiply: y + 3 = -6x - 54
Subtract: y = -6x -57
Answer:
y=-6x-57 (this answer is in slope-intercept form)
I don't know what your choices are and if you can select multiple answers or not.
Step-by-step explanation:
y=mx+b is an equation for a line with slope m and y-intercept b.
We are given m=-6 so we will plug this in giving us: y=-6x+b.
Now we need to find b, the y-intercept. Let's use a point (x,y) we know is on the line of y=-6x+b to find b.
We know (x,y)=(-9,-3) is on that line. So our line should satisfy this point. We must pick a b so that happens. Plug (x,y)=(-9,-3) into the equation now.
-3=-6(-9)+b
-3=54+b
-3-54=b
-57=b
So the equation is y=-6x-57
2 Polnts
If f(x)=2(x)2 +5/(x+2), complete the following statement:
f(2)=-
Answers
Answer:
[tex]f(2)=\frac{37}{4}[/tex] or [tex]f(2)=-(-\frac{37}{4})[/tex]
Step-by-step explanation:
we have
[tex]f(x)=2x^{2} +\frac{5}{x+2}[/tex]
Find f(2)
we know that
f(2) is the value of f(x) when the value of x is equal to 2
so
For x=2
substitute
[tex]f(2)=2(2)^{2} +\frac{5}{2+2}[/tex]
[tex]f(2)=8 +\frac{5}{4}[/tex]
[tex]f(2)=\frac{37}{4}[/tex]
or
[tex]f(2)=-(-\frac{37}{4})[/tex]
In the figure, AB || DE. Find the measure of Z.
Answers
Answer:
x is 50 degrees
Step-by-step explanation:
If you subtract 65 twice from 180 you get this answer. The line is a straight line making it equal 180 degrees
The correct answer is 50
Español
Brian needs to memorize words on a vocabulary list for Spanish class.
He has memorized 24 of the words, which is three-fourths of the list.
How many words are on the list?
Answers
Answer:
There are 32 words total on the list.
Step-by-step explanation:
24*4=96;
96÷3=32;
There are 32 words total on the list.
Answer:
gfrwkmsvfbs
Step-by-step explanation:
dfffve
The area of a rectangle with width x and length 5x is 5x2. What does the coefficient 5 mean in terms of the problem?
Answers
Answer:
The length is 5 times the width
Step-by-step explanation:
Let
W ----> the width of the rectangle
L ----> the length of the rectangle
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
In this problem we have
[tex]L=5x[/tex] ----> equation A
[tex]W=x[/tex] ----> equation B
substitute equation B in equation A
[tex]L=5W[/tex]
therefore
The length is 5 times the width
Marta was pregnant 268 days, 258 days, and 271 days for her first three pregnancies. in order for marta’s average pregnancy to equal the worldwide average of 266 days, for how long must her fourth pregnacy last? for Marta's average pregnancy to equal the worldwide average of 266 days, for how long must her fourth pregnancy last?
Answers
To find the average, you add all of the numbers and divide by the number of numbers (If that makes sense)
We can use variables (x) to solve for the last number.
268+258+271+x/4 = 266
Multiply both sides by 4
268+258+271+x = 266*4
268+258+271+x = 1064
Add the three numbers together
797+x = 1064
Subtract both sides by 797
x = 267
Her fourth pregnancy must last 267 days.
Answer:
267
Step-by-step explanation:
So we want to find the average of 4 numbers:
268, 258, 271, and x
The average of those 4 numbers is represented by the fraction:
[tex]\frac{268+258+271+x}{4}[/tex]
Now we also wanting this average to be equal to 266. We need to find x such that that happens.
So we have the following equation to solve:
[tex]\frac{268+258+271+x}{4}=266[/tex]
Multiply both sides by 4:
[tex]268+258+271+x=4(266)[/tex]
Do any simplifying on both sides:
[tex]797+x=1064[/tex]
Subtract 797 on both sides:
[tex]x=1064-797[/tex]
Simplify:
[tex]x=267[/tex]
PLEASE HELP WITH MATH QUESTION!!
The largest angle in a triangle is equal to the sum of the two other angles. The middle angle is twice the measure of the smallest angle. What is the measure of each angle?
A)32°, 64°, 90°
B)30°, 60°, 80°
C)30°, 60°, 90°
D)30°, 60°, 100°
Answers
in triangle ABC, angle A = 45, c= 17, and angle B = 25. Find a to the nearest tenth.
Answers
Answer:
The answer would be 12.8
Step-by-step explanation:
I looked it up and found the answer on another website
it is 12.8
By using the sine rule we got the value of a is 8 units.
Given that, in triangle ABC, angle A = 45, c= 17, and angle B = 25.
We need to find the measure of side a.
What is the sine rule?The sine rule formula is sinA/a=sinB/b=sinC/c.
Now, sin45°/a=sin25°/b=sin110°/17
⇒sin45°/a=0.9397/17
⇒0.7071/a=0.0854
⇒a=8.27≈8
Therefore, the value of a is 8 units.
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3. Simplify the square root.
-{144}
Answers
Answer:
12
Step-by-step explanation:
The number 144 can be factorized as = 2*2*2*2*3*3= (4^2)* (3^2)
Therefore, sqrt(144)= sqrt((4^2)* (3^2))= sqrt{(4*3)^2= sqrt{12^2}=12
Is 24/40=4/7 a true proportion? Justify your answer
Answers
A proportion
[tex]a\div b = c\div d[/tex]
is nothing but a comparison between two fractions: we can rewrite it as
[tex]\dfrac{a}{b}=\dfrac{c}{d}[/tex]
So, we can multiply both sides by the two denominators b and d to get
[tex]\dfrac{a}{b}=\dfrac{c}{d} \iff ad = bc[/tex]
In other words, a proportion is true if the product of the inner terms is the same as the product of the outer terms.
In your case, we have the check is the following:
[tex]24 \div 40 = 4\div 7 \iff 24\cdot 7 = 40\cdot 7 \iff 168 = 280[/tex]
which is clearly false. So, 24:40 = 4:7 is not a true proportion. In fact, if we convert fractions into numbers, we have
[tex]\dfrac{24}{40} = 0.6,\quad \dfrac{4}{7} = 0.\overline{571428}[/tex]
which makes even more clear that the proportion doesn't hold.
what is the solution to √3x+54 + 6 = 10
Answers
Answer:
x = -(38/3)
Step-by-step explanation:
Well first you have to isolate the square root on the left hand side.
Then eliminate the radical on the left hand side.
Last step
Solve the linear equation :
Rearranged equation
3x + 38 = 0
Subtract 38 from both sides
3x = -38
Divide both sides by 3
A possible solution is :
x = -(38/3)
For this case we must solve the following equation:
[tex]\sqrt {3x + 54} + 6 = 10[/tex]
Subtracting 6 from both sides of the equation:
[tex]\sqrt {3x + 54} = 10-6\\\sqrt {3x + 54} = 4[/tex]
We square both sides of the equation squared:
[tex]3x + 54 = 4 ^ 2\\3x + 54 = 16[/tex]
We subtract 54 from both sides of the equation:
[tex]3x = 16-54[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]3x = -38[/tex]
We divide between 3 on both sides:
[tex]x = \frac {-38} {3}\\x = - \frac {38} {3}[/tex]
Answer:
[tex]x = - \frac {38} {3}[/tex]
what transformation of the parent function, f(x) = x^2, is the function f(x) = -(x + 2) ^2
Answers
Answer:
f(x) reflects across the x-axis and translate left 2 ⇒ 2nd answer
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new
function g(x) = f(-x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Lets solve the problem
∵ f(x) = x²
∵ The parent function is f(x) = - (x + 2)²
- There is a negative out the bracket means we change f(x) to -f(x)
∴ f(x) is reflected across the x-axis
- The x is changed to x + 2, that means we translate the f(x) to the
left two units
∵ x in f(x) is changed to (x + 2)
∴ f(x) is translated 2 units to the left
∴ f(x) reflects across the x-axis and translate left 2
The function f(x) = -(x + 2) ^2 is a reflection over the x-axis and a horizontal shift to the left by 2 units.
Explanation:The given function, f(x) = -(x + 2) ^2, is a transformation of the parent function, f(x) = x^2. The negative sign in front of the function reflects it over the x-axis, making it an upside-down parabola. The addition of 2 inside the parentheses shifts the graph 2 units to the left. Therefore, the transformation is a reflection over the x-axis and a horizontal shift to the left by 2 units.
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Help please
3^4 + 4 ⋅ 5 = ____. (Input whole numbers only.) (20 points)
Answers
Answer:
101
Step-by-step explanation:
3^4 = 81
4 x 5 20
81 +20 = 101
Answer:
101
Step-by-step explanation:
[tex]3^{4}[/tex] = 81 and 4 x 5 =20, so 20+81= 101.
Charlie paints the figure shown on the sign of his new restaurant. The figure is made from a circle with a sector missing. What is the area of the painted part of the figure, shown here as the shaded part?
Answers
Answer:
12.5
Step-by-step explanation:
divide 25 by 2
To find the area of the painted part, subtract the area of the missing sector from the area of the entire circle.
Explanation:The area of the painted part of the figure can be found by subtracting the area of the missing sector from the area of the entire circle. To find the area of the missing sector, we need to know the central angle of the sector. Once we have the central angle, we can use the formula for the area of a sector to calculate the area of the missing sector. Finally, we subtract the area of the missing sector from the area of the entire circle to find the area of the shaded part.
Example:
If the circle has a radius of 5 units and the central angle of the missing sector is 60 degrees, we can calculate:
Area of missing sector = (60/360) * π * 5^2
Area of the shaded part = π * 5^2 - (60/360) * π * 5^2
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Which property is 7x +(4x + 1) = (7x + 4x) + 1t
Answers
Answer:
associative property
Step-by-step explanation:
This illustrates the associative property. It doesn't matter in which order you combine the terms here.
This is an example of associative property which states,
[tex]a+(b+c)=(a+b)+c[/tex]
Hope this helps.
r3t40
Joseph has started completing the square on the equation 3x2 - 7x + 12 = 0. He has worked to the point where he has the expression x2 - x = -4. Use complete sentences describe Joseph’s steps up to this point and whether or not his work is accurate.
Answers
Answer:
x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6 thus NO, x^2 - (7 x)/3 = -4 would be correct.
Step-by-step explanation:
Solve for x:
3 x^2 - 7 x + 12 = 0
Hint: | Write the quadratic equation in standard form.
Divide both sides by 3:
x^2 - (7 x)/3 + 4 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 4 from both sides:
x^2 - (7 x)/3 = -4
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 49/36 to both sides:
x^2 - (7 x)/3 + 49/36 = -95/36
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 7/6)^2 = -95/36
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 7/6 = (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6
Hint: | Look at the first equation: Solve for x.
Add 7/6 to both sides:
x = 7/6 + (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6
Hint: | Look at the second equation: Solve for x.
Add 7/6 to both sides:
Answer: x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6
Answer:
Joseph's work wasn't accurate
Step-by-step explanation:
Take a look at the image to understand the procedures
What negative 5 plus 3 equal using a number line
Answers
Answer:
the answer is -2 and would be plotted on -2 on a number line
Can someone help me with this assignment, please? I will give out 65 points and Brainliest!
I'm so confused by this assignment and any help would be appreciated.
Answers
Step-by-step explanation:
The first polygon, ABCD, should be rotated around DA' axis and then create a function f'(x)=f(x) +5 to transpose ABCD poligon into A'B'C'D' position
The second polygon, MNOP, rotate around MP axis and half the size ( Area)
Step-by-step explanation:
1b) First, reflect ABCDE over the x-axis.
(x, y) → (x, -y)
Then, translate 5 units to the right and 3 units down.
(x, -y) → (x+5, -y-3)
1c) Instead of reflecting over the x-axis, we can reflect ABCDE over the y-axis.
(x, y) → (-x, y)
Then, rotate about the origin 180 degrees.
(-x, y) → (x, -y)
Finally, translate 5 units to the right and 3 units down.
(x, -y) → (x+5, -y-3)
2b) First, rotate MNOP 90 degrees clockwise about the origin.
(x, y) → (y, -x)
Then, scale by 1/2.
(y, -x) → (y/2, -x/2)
Finally, translate 3.5 units to the left and 2.5 units down.
(y/2 - 3.5, -x/2 - 2.5)
2c) We can form a second method by changing the order of transformations.
First translate MNOP 5 units to the right and 7 units down.
(x, y) → (x + 5, y - 7)
Then scale by 1/2.
(x + 5, y - 7) → (x/2 + 2.5, y/2 - 3.5).
Finally, rotate 90 degrees about the origin.
(y/2 - 3.5, -x/2 - 2.5)
3b) First, rotate EFGH 45 degrees counterclockwise about the origin.
(x, y) → (½√2 (x - y), ½√2 (x + y))
Then scale by ⅓√2.
(½√2 (x - y), ½√2 (x + y)) → (⅓ (x - y), ⅓ (x + y))
Finally, translate 13/3 units to the right and 1 units down.
(⅓ (x - y), ⅓ (x + y)) → (⅓ (x - y) + 13/3, ⅓ (x + y) - 1)
3c) Again, we can form a second method by changing the order of the transformations.
Let's keep the first step the same, rotating EFGH 45 degrees counterclockwise about the origin:
(x, y) → (½√2 (x - y), ½√2 (x + y))
Then translate 13/√2 units to the right and 3/√2 units down.
(½√2 (x - y), ½√2 (x + y)) → (½√2 (x - y) + 13/√2, ½√2 (x + y) + 3/√2)
Finally, scale by ⅓√2.
(½√2 (x - y) + 13/√2, ½√2 (x + y) + 3/√2) → (⅓ (x - y) + 13/3, ⅓ (x + y) + 1)
4b) First, rotate XYZ 45 degrees clockwise about the origin.
(x, y) → (½√2 (x + y), ½√2 (y - x))
Then translate 5-√2 units to the right and 4√2 units up.
(½√2 (x + y), ½√2 (y - x)) → (½√2 (x + y) + 5 - √2, ½√2 (y - x) + 4√2)
4c) Instead, let's translate XYZ 5 units to the left and 3 units up.
(x, y) → (x - 5, y + 3)
Then rotate 45 degrees clockwise about the origin:
(x - 5, y + 3) → (½√2 (x + y - 2), ½√2 (y - x + 8))
Finally, translate 5 units to the right.
(½√2 (x + y - 2), ½√2 (y - x + 8)) → (½√2 (x + y - 2) + 5, ½√2 (y - x + 8))
a piece of paper, graph y> 2x.Then determine which answer matches the graph you drew.
Answers
To graph the equation y > 2x, start by graphing the line y = 2x and shading the region above it.
Explanation:To graph the equation y > 2x, we start by graphing the line y = 2x. This line has a positive slope (b > 0) and passes through the origin (0, 0). Since we want to graph y > 2x, we need to shade the region above the line.
Draw the line y = 2x as a solid line. Then, shade the region above the line to indicate that y is greater than 2x.
Answer: Graph (a) matches the given inequality y > 2x.
Learn more about Graphing Linear Inequalities here:https://brainly.com/question/38474175
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(5ab - 10b^2 + 15bc) ÷ 5b
Answers
Answer:
Final answer: a-2b+3c
Step-by-step explanation:
5ab/5b= a
-10b^2/5b= -2b
15bc/5b= 3c
Answer:
a - 2b + 3c
Step-by-step explanation:
Factor the numerator by factoring out 5b from each term, that is
[tex]\frac{5b(a-2b+3c)}{5b}[/tex]
Cancel the 5b on the numerator/ denominator, leaving
a - 2b + 3c
In ∆ABC, ∠A is a right angle and m∠B = 45°. Find BC.
Answers
Step-by-step explanation:
In ∆ABC, if <A is 90° and <B is 45° then hypotenuse is BC.
Now,
Cos B= base/height
Cos B= AB/ BC
BC= AB/cos 45°.
Answer:
17 sqrt 2
Step-by-step explanation:
trust me the length is 24.04163 which equals 17√2
www.calculator.net has a triangle calculator if u think im wrong just look up triangle calculator
a cereal box has a length of 8 inches, a width of 1 3/4 inches, and a height of 12 1/8. What is the surface area of the box?
Answers
Answer:
270 7/16 in^2.
Step-by-step explanation:
The surface area equals the sum of the areas of 3 pairs of congruent rectangles.
These are 2 * 8 * 1 3/4 + 2 * 8 * 12 1/2 + 2 * 1 3/4 * 12 / 1/8
= 16 * 7/4 + 16 * 25/2 + 2 * 7/4 * 97/8
= 28 + 200 + 42 7/16
= 270 7/16 in^2.
Select the equivalent expression.
(a^5 * 2^3)^3 = ?
1. a^8*2^9
2. a^15*2^6
3. a^8*2^6
3. a^15*2^9
Answers
Answer:
a^15 * 2^9
Step-by-step explanation:
(a^5 * 2^3)^3 =
= (a^5)^3 * (2^3)^3
= a^(5 * 3) * 2^(3 * 3)
= a^15 * 2^9
Answer: the second choice 3.
Answer:
3. a^15*2^9
Step-by-step explanation:
We know that (a * b) ^c = a^c * b^c
(a^5 * 2^3)^3
a^5^3 * 2^3^3
And we know that a^b^c = a^(b*c)
a^(5*3) * 2^(3*3)
a^15 * 2^9