Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.
T=
U=
V=
W=
Answers
The coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:
T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)
When a point P(x, y) is rotated 270° counterclockwise around the origin, we flip x and y and reverse the sign of x.
Thus,
The rule to rotate a point P(x, y) after a rotation 270° counterclockwise around the origin is:
P(x, y) → P'(y, -x)
From the Graph,
In our case, we have the points
T = (4, -8)
U = (6, -8)
V = (9, -3)
W = (7, -3)
Thus, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:
P(x, y) → P'(y, -x)
T (4, -8) → T'(-8, -4)
U (6, -8) → U'(-8, -6)
V (9, -3) → V'(-3, -9)
W (7, -3) → W'(-3, -7)
Therefore, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:
T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)
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Related Questions
−12+(−20)
Enter your answer in the box.
Answers
Answer:-32
Step-by-step explanation:
-12+(-20)
-12-20
-32
Answer: -32
Step-by-step explanation:
−12+(−20)=
-12 - 20= ==> adding a negative number is equal to subtracting by the positive version of that number. ?-20=?+(-20)
-(12+20)=-32
help meeeeeeeeeeeeeee pleaseee
Answers
The vertex of the graph is (2, -1), the axis of symmetry of the graph is x = 2 and the parabola opens downward
How to determine the properties of the function?The vertex
The graph represents the given parameter
From the graph, we can see that:
The maximum point on the graph is located at
(2, -1)
The vertex of a graph is the maximum or the minimum of the graph
This means that
Vertex = (2, -1)
The axis of symmetry
The graph represents the given parameter
In (a), we have
Vertex = (2, -1)
Remove the y-coordinate
x = 2
The axis of symmetry of a graph is the x coordinate of the vertex
This means that the axis of symmetry is x = 2
The direction of the parabolaFrom the graph, we can see that the parabola opens downward
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A tortoise and a hare run in the NYC marathon (26.2 miles). The hare crosses the finish line first in a time of 4 hours and 30 minutes. How fast did the hare run?
Answers
The hare ran 5.8 mph to win the race.
What is Speed?Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.
Given that, a tortoise and a hare run in the NYC marathon for 26.2 miles, the hare crosses the finish line first in a time of 4.5 hours.
Speed = distance/time
Speed of hare = 26.2/4.5 = 5.8 mph
Hence, The hare ran 5.8 mph to win the race.
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PLEASE HELP!
4) The "random walk theory of stock prices holds that price movements in disjoint time periods are independent of each other. Suppose that we record only whether the price is up or down each year, and that the probability that our portfolio rises in price in any one year is 0.65.
a) What is the probability that the portfolio goes up for 3 consecutive years?
b) What is the probability that the portfolio's value moves in the same direction (either up or down) for 3 consecutive years?
c) What is the probability that the portfolio's value goes up for at least 1 of 3 years?
Answers
Part (a)
Each year is independent of any other. This allows us to simply multiply the probability values for each increase. Recall that P(A and B) = P(A)*P(B) if and only if events A & B are independent.
(0.65)*(0.65)*(0.65) = (0.65)^3 = 0.274625
Answer: 0.274625=========================================
Part (b)
We calculated the probability of an increase for each of the 3 years back in part (a). Let's calculate we have a decrease 3 times in a row.
0.65 is the probability of increase for any given year, which makes 1-0.65 = 0.35 the probability of decrease for any given year.
Therefore (0.35)^3 = 0.042875 represents the probability of 3 decreases in a row.
Add this result to what we got in part (a)
0.274625+0.042875 = 0.3175
This is done because we could have 3 increases OR 3 decreases (pick one). Think of it like this P(A or B) = P(A) + P(B) where A & B are mutually exclusive events.
Answer: 0.3175=========================================
Part (c)
In the previous part we calculated 0.042875 as the probability of 3 decreases in a row.
1-0.042875 = 0.957125 is the probability of at least one increase. Note how the events "no increases" and "at least one increase" are complementary events. They are opposite. One or the other must happen, which allows us to subtract from 1.
You can think of it like this
P(no increases) + P(at least one increase) = 1
P(at least one increase) = 1 - P(no increases)
Answer: 0.957125Side note: none of the final answers have been rounded.
please I need help asap
Answers
x=-1 , y= -3.5
x=0 , y= -3
x=1 , y= -2.5
x=2 , y= 4
just plug in the x value into the equation where you see x and you’ll get your answer. for example:
the first one where x is -2:
y= 0.5(-2) - 3
y= -4
and the same goes for every one of them
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
The equation of the parabola
f(x) = [tex]7x^2[/tex]
The standard vertex form of a parabola is
y = [tex]a(x-h)^2[/tex] + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) = [tex]7x^2[/tex]
The value of a = 7
Substitute the values in the vertex form of a parabola
y = [tex]7(x-3)^2[/tex] + 5
Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
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Last year, the student population at Haley Elementary School was 360 students. After rezoning this year, the student population is 10% smaller. HOW MANY STUDENTS ATTEND HALEY ELEMENTARY THIS YEAR?
Answers
Answer:
360 of 10%
360 x 10/100
36
now, 360 - 36 = 324
therefore, 324 students attended haley elementry this yr.
f(x) = 11 – x Find the range of f for x > 4.
Answers
Answer:
Step-by-step explanation:
Comment
The graph below shows or implies that you start at very close to 4 and move downward and to your right
To find the beginning of the range, substitute 4 into the given equation
f(4) = 11 - 4
f(4) = 7
The range is
7 <y <-∞
What is the remainder of the following division problem?
x StartLongDivisionSymbol x + 1 EndLongDivisionSymbol. minus x to get a remainder of 0 + 1 and a quotient of 1.
x
1
0
–1
Answers
The remainder of the long division problem (x + 1)/x is given as follows:
1.
What is a long division?The representation of a long division problem is given as follows:
di(x)/d(x) = q(x) + (r(x)/b(x))
In which the meaning of each symbol is listed as follows:
di(x) is the dividend of the division operation.d(x) is the divisor of the division operation.q(x) is the quotient of the division operation.r(x) is the remainder of the division operation.In the context of this problem, the operation is presented as follows:
(x + 1)/x.
This division can be separated into two divisions that are added, hence:
(x + 1)/x = x/x + 1/x = 1 + 1/x.
Comparing to the standard symbols, we have that:
The quotient of the division operation is of 1.The remainder of the division operation is of 1.Missing informationThe expression is:
(x + 1)/x.
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Answer:
B 1
Step-by-step explanation:
given: line 1 passes through (-3, -7) and (5,3)
Line 2 passes through (-4, -2) and is perpendicular to line 1
Answers
Answer:
Step-by-step explanation:
We start by developing an equation for Line 1, and then use that to find the equation for Line 2. We'll use the form of an equation for a straight line:
y = mx + b,
where m is the slope and b the y-intercept (the value of y when x=0).
Line 1
Determine the slope, m, by calculating the "Rise/Run" between the two points (-3,-7) and (5,3).
Line up the two points from left to right (based on x) and then calculate:
Rise: (3 - (-7)) = 10
Run: (5 -(-3) = 8
The slope, m, is Rise/Run or (10/8)
The equation becomes y = (5/4)x + b
We could calculate b, the y-intercept, by entering one of the two given points and solving for b, but the only thing we need from this line is it's slope, m. Slope is (5/4), which we'll use in the next step: Line 2.
[Note: Out of curiosity, here is the calculation for b: Use point (5,3) in y = (5/4)x + b and solve for b. 3 = (5/4)*5 + b. 3 = (25/4) + b b = -13/4. This means that Line 1 is y = (5/4)x -(13/4)]
Line 2
The slope of a line perpendicular to the first is the "negative inverse" of the first line. In this case, line 1's slope of (13/8) would become a slope of -(8/13) for line 2.
Line 2: y = -(8/13)x + b
We'll calculate b for this line by enetering the single point provided, (-4,-2), and solving for b:
y = -(8/13)x + b
-2 = -(8/13)*(-4) + b
-2 = (32/13) + b
-2 - (32/13) = b
b = -(26/13) - (32/13)
b = -(58/13)
The new line perpendicular to Line 1 and passing through (-4,-2) is:
y = -(8/13)x -(58/13)
See attached graph.
a plane has a cruising speed of 250 miles per hour when there is no wind. at this speed, the plane flew miles with the wind in the same amount of time it flew miles against the wind. find the speed of the wind.
Answers
The speed of the wind is 50 mph.
Define speed.Speed, expressed in terms of meters per second, is the rate at which an object's position changes. A thing moves one metre in one second, for instance, if it starts at the origin and moves three metres in three seconds. The formula for speed is as straightforward as dividing a distance by a time.
Given,
250 mph for the plane's speed when there is no wind
v is the wind speed.
Think about how the plane will move against the wind:
V' = the rate of flight of the aircraft against the wind = V + v = 250 + v
300 miles is the distance travelled in d'.
T is the passage of time over the distance.
The distance's travel time is specified as
t' = d'/V'
t' = 300/(250 + v) eq-1
Think about how the plane moves when flying against the wind:
V" is the speed of a plane travelling against the wind and equals V - v. This equals 250 - v.
D" = 200 miles of distance travelled
t" is the passage of time over the distance.
The distance's travel time is specified as
t'' = d''/V''
t'' = 200/(250 - v) eq-2
Due to this:
travelling time of 300 time required to drive 200 miles in miles
t' = t''
using eqs 1 and 2
300/(250 + v) = 200/(250 - v) (250 - v)
3/(250 + v) = 2/(250 - v) (250 - v)
750 - 3 v = 500 + 2 v
5 v = 250
v = 50 mph
The speed of the wind is 50 mph.
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List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
Answers
The reduced fraction is 7 using GCF method.The GCF is also known as the Highest Common Factor (HCF)
What is GCF method?The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)
The fraction = 14/66
The factors of 14 = 2×2×2×3
The factors of 28 = 11*3*2
The gcf is 2 × 2 = 4
Divide the denominator and numerator by 4
14 ÷2 = 7
14÷ 2 = 7
We get,
The fraction = 14/2 =7
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-2(7+3m) +6m>3 (3m-5)
Answers
Answer:
1/9 > m
Step-by-step explanation:
-2(7+3m)+6m>3(3m-5)
Distribute.
-14-6m+6m>9m-15
Combine like terms.
-14>9m-15
1>9m
Get m to be alone.
1/9>m
Question :
-2(7+3m) + 6m > 3(3m-5)
-2(3m+7) + 6m > 3(3m-5)
-6m - 14 + 6m > 9m - 15
Next, let we combine it
-14 > 9m - 15
After that, let add 15 to both sides
-14 + 15 > 9m - 15 + 15
1 > 9mNext, we will divide both sides by the same factor
1/9 > 9m/9Lastly we will cancel the terms that are both in the numerator and denominatorMove the variable to the left and flip the inequality
m < 1/9
The final answer is m < 1/9
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Which of the following equations have infinitely many solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-6x+35=-6x-35−6x+35=−6x−35minus, 6, x, plus, 35, equals, minus, 6, x, minus, 35
(Choice B)
B
-6x+35=-6x+35−6x+35=−6x+35minus, 6, x, plus, 35, equals, minus, 6, x, plus, 35
(Choice C)
C
6x+35=-6x+356x+35=−6x+356, x, plus, 35, equals, minus, 6, x, plus, 35
(Choice D)
D
6x+35=-6x-356x+35=−6x−356, x, plus, 35, equals, minus, 6, x, minus, 35
Answers
The equation which has infinitely many solutions include the following: B. -6x + 35 = -6x + 35
What are infinitely many solutions?In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal.
This ultimately implies that, an equation would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and intercept for the two lines are the same.
In this scenario, we can reasonably and logically deduce that the following equations satisfy the condition for an equation which has infinitely many solutions:
-6x + 35 = -6x - 35 (False).
-6x + 35 = -6x + 35 (True).
6x + 35 = -6x + 35 (False).
6x + 35 = -6x - 35 (False).
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Complete Question:
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
A. -6x + 35 = -6x - 35
B. -6x + 35 = -6x + 35
C. 6x + 35 = -6x + 35
D. 6x + 35 = -6x - 35
Ty bought three and four-sixths pounds of coffee. He gave five-sixths of a pound to his grandma. Estimate how much coffee Ty has left.
5 pounds
four and one-half pounds
3 pounds
two and one-half pounds
Answers
Ty has 2 5/6 pounds of coffee left after giving 5/6 pounds of coffee to his grandma
What is fraction?Fraction is a numerical quantity that is not a whole number
From the question,
Ty bought 3 4/6 pounds of coffee
converting 3 4/6 to improper fraction
we have 22/6
Ty gave his friend 5/6 pound of coffee to his grandma
To estimate how much coffee Ty has left
We substract Coffee given to his grandma from Coffee bought
That is,
22/6 - 5/6
= 17/6
= 2 5/6 pounds of coffee left
Ty has 2 5/6 pounds of toffee left. He gave 5/6 of what he bought to his grandma.
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15÷(3+13)2 i need help
Answers
Answer: 47
Step-by-step explanation:
help ASAP 20 points and will mark you brainleast
Solve the system of equations by the addition method.
look at the image ---->
Answers
Answer:
x=3 y=4
Step-by-step explanation:
-4x= -6y+12 -1
8x-4y = 8 -2
-4x+6y=12 -1
8x-4y = 8 -2
multiply first equation by 2:
2(-4x+6y=12)
= -8x+12y=24
add with 2nd equation;
-8x+12y=24
+
8x-4y=8
-8x+8x=0
+12-4y=8y
24+8=32
0+8y=32
y=32/8
y=4
input y into any equation to get x:
-4x= -6(4)+12
-4x = -24+12
-4x= -12
-x= -12/4
x=3
83.978, 78.934, 84.765 Underline the thousandths digit in each number
help meee pleaseeee
Answers
Answer:
83.978 the thousandth digit is 3, 78.934 the thousandth digit is 8,84.765 the thousandth digit is 4
Answer:
Step-by-step explanation:
Ok:
1. Identify the thousandths digit
The numbers to the left of the decimal point are the ones and hundreds digits
The first number to the right of the point is the tenths digits
The second to the right of point i s the Hundreths
The third number to the right of point is the thounsandths which is what we are looking for!
2. Apply to problem!
1. 83.978 : Thousandths digit is 8
2. 78.934 : Thousandths digit is 4
3. 84.765 : Thousandths digit it 5
Extra tips and tricks writing as fractions!Ps: Some are not simplified!
1. 83.978= 83 978/1000 as fraction
2. 78.932= 78 932/1000 as fraction
3. 84.765= 84 765/1000 as fraction
the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing (in mm3/s) when the diameter is 80 mm? (round your answer to two decimal places.)
Answers
Increase in volume is 802424.77 cubic mm/s when the diameter is 80 mm.
Let the radius of the sphere be R.
So, the volume of the sphere is given by,
V = [tex]\frac{4}{3}\pi r^3[/tex]
Differentiating the above relation with respect to time 't' we get,
dV/dt = 4[tex]\pi r^2[/tex]. dr/dt
Given that, the change of radius (dr/dt) = 4 mm/s
When the diameter is 80 mm, then the radius = 80/2 = 40 mm
So the volume change when the diameter is 80 mm is given by,
dV/dt [tex]=4\pi\times40^2\times4\approx 802424.77[/tex] cubic mm/s
Hence the volume increase in 802424.77 cubic mm/s.
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Step 1 5x + 9 = 2x - 3
Step 2 3x + 9 = -3
Step 3 3x = -12
Step 4 x = -4
What operation did he perform to get from step 1 to step 2
Answers
Answer:
He subtracted a term of [tex]2x[/tex] from both sides of the equation.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The point -3/5 , -4/5 in the third quadrant corresponds to angle θ on the unit circle.
The value of sec θ is ____
, and the value of cot θ is _____
.
Answers
The value of sec θ is -5/3 ,and the value of cot θ is 3/4 in the unit circle.
Given:
The point -3/5 , -4/5 in the third quadrant corresponds to angle θ on the unit circle.
here x = -3/5 and y = -4/5
radius r = [tex]\sqrt{(-3/5)^{2}+(-4/5)^{2} }[/tex]
= [tex]\sqrt{9/25 + 16/25}[/tex]
r = 1.(which is hypotenuse in unit circle).
sec θ = hypotenuse / adjacent
= 1/-3/5
sec θ = -5/3
cot θ = adjacent / opposite
= -3/5 / -4/5
= 3*5/5*4
= 15/20
cot θ= 3/4
Therefore the value of sec θ is -5/3 ,and the value of cot θ is 3/4.
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mike discovered that the pool in his backyard is leaking slowly. the pool holds 15,478 gallons of water, and is leaking at a rate of 11 gallons per day. if mike does not replace the water that has leaked from the pool, how many gallons of water will remain in the pool after 91 days?
Answers
The pool will have 14, 477 gallons of water.
The amount of water that has leaked in 91 days = rate of leakage × number of days
Keep the values in formula
The amount of water that has leaked in 91 days = 11 × 91
Performing multiplication
The amount of water that has leaked in 91 days = 1001 gallons
Amount of water remaining after 91 days = total amount of water - the amount of water that has leaked in 91 days
Amount of water remaining after 91 days = 15,478 - 1001
Performing subtraction
Amount of water remaining after 91 days = 14, 477 gallons
Hence, after 91 days there will be 14, 477 gallons of water in the pool.
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There are 14 students in the school that like vanilla ice cream best. This represents 20% of the total number of students at the school. How many students are there in the school in total?
Answers
There are 70 students in the school in total
Arun spends some of the money from his monthly salary on food, travelling and entertainment and the rest of the money he deposits in the bank. (i) The money he spends on food, travelling and entertainment is in the Ratio, food : travelling : entertainment = 4 : 2 : 3. If he spends on food $160 more than travelling calculate the amount he spends on entertainment.
(c) If he deposits 1/7 of his monthly salary , calculate his monthly salary
Answers
The amounts are given as follows, using proportions:
i) Amount spent on entertainment: $240.
c) Monthly salary: $840.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem along with basic arithmetic operations such as multiplication or division to find the desired amounts.
The ratio of food : travelling : entertainment = 4 : 2 : 3 means that:
4/9 of the investment was in food.2/9 of the investment was in travelling.3/9 of the investment was in entertainment.The amount spent on food $160 more than travelling, the total amount is obtained as follows:
(4/9 - 2/9)x = 160
2/9x = 160
2x = 160 x 9
x = 80 x 9
x = 720.
Then the amount invested in entertainment was of:
3/9 x 720 = 1/3 x 720 = $240.
He invests 6/7 of his monthly salary, as 1/7 is deposited, hence:
6x/7 = 720
6x = 720 x 7
x = 120 x 7 (simplifying both sides of the equality by 6)
x = $840.
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The volume of the triangular prism is 12.5 m³. The length is 2.5 m and the base is 2 m. What is the width?
Answers
Answer: 4.5m
Step-by-step explanation:
because 12.5 can - by 2.5
then 9.0=9 -5.5=4.5
explanation: I also did this and got it right
5. A rectangular 52 inch flat screen TV has a length of 42 inches. The salesman explains that all TV's are sold by the length of the diagonal. So, a 52 inch flat screen TV actually has a diagonal measure of 52 inches. To the nearest whole inch, what is the height of the TV?
Answers
The height of the TV is 31 inches . This can be calculated using Pythagoras theorem.
What is Pythagoras theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Main Body:
according to the question --
hypotenuse = 52 in
base = 42 in
height =?
Pythagoras theorem = [tex]{P^{2} +B^{2} }[/tex] = [tex]H^{2}[/tex]
inserting the values --
52² = 42² +H²
H² = 2704- 1764
H² = 940
H≈31 inches
Hence the height of TV is 31 inches
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Graph the image of △IJK after the following sequence of transformations:
Translation 17 units left and 5 units up
Reflection across the line y=1
Answers
Please find attached the graph of the image of ΔIJK following a translation transformation of (-17, 5), and a reflection across the line y = 5
What is a transformation in geometry?A transformation is an operation that changes the location, size and shape of geometric figures.
The coordinates of the vertex of ΔIJK are; I(14, 8), J(8, 5), K(14, 2)
The translation transformation is 17 units left and 5 units up = T₍₋₁₇, ₅₎
The location of the vertices of the image of ΔIJK following the translation transformation are;
[tex]I(14,\, 8)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ I'(-3,\, 13)[/tex]
[tex]J(8, 5)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ j'(-9,\, 10)[/tex]
[tex]K(14, 2)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ K'(-3,\, 7)[/tex]
The coordinates of a point following a reflection across the line y = 1 are as follows;
The coordinates of the vertices of the image I'J'K' relative to the line y = 1 are;
I'(-3, 13), Relative point I'(-3, 12)
J'(-9, 10) has a relative point at (-9, 9)
K'(-3, 7) has a relative point (-3, 6)
The coordinates of the vertices of the reflected image are therefore;
(x, y) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] (x, -(y - 1))
Which gives;
I'(-3, 12) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-3, -12 + 1) = I''(-3, -11)
J'(-9, 9) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-9, -9 + 1) = I''(-9, -8)
k'(-3, 6) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] k''(-3, -6 + 1) = k''(-3, -5)
Please find attached the image of the ΔIJK following the translation and reflection transformation
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Dividing the polynomial P(x) by x + 2 yields a quotient Q(x) and a remainder of 8. If Q(2) = 5, find P(-2) and p(2)
Answers
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Explanation:
Part A) Find P(-2)
We'll divide P(x) over (x+2) to get a quotient Q(x) and remainder 8 like so
P(x)/(x+2) = quotient + remainder/(x+2)
P(x)/(x+2) = Q(x) + 8/(x+2)
When multiplying both sides by (x+2), it clears out the fractions and we're left with this
P(x) = (x+2)*Q(x) + 8
From here, plug in x = -2 and simplify
P(x) = (x+2)*Q(x) + 8
P(-2) = (-2+2)*Q(-2) + 8
P(-2) = (0)*Q(-2) + 8
P(-2) = 0 + 8
P(-2) = 8
Luckily we don't need the value of Q(-2) since it cancels out with the zero.
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Part B) Find P(2)
This time we'll plug in x = 2 and we'll get...
P(x) = (x+2)*Q(x) + 8
P(2) = (2+2)*Q(2) + 8
P(2) = 4*Q(2) + 8
P(2) = 4*5 + 8
P(2) = 20+8
P(2) = 28
Identify x-intercepts, the vertex, and axis of symmetry of the graph f(x)= 1/4x (x-1)(x+7)
Answers
x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
What is, axis of symmetry, vertex and x - intercept?
A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.
A line's x-intercept is the location at which the x-axis is crossed.
Consider, the given equation,
[tex]f(x) = \frac{1}{4}(x - 1)(x + 7)[/tex]
Let,
[tex]y = \frac{1}{4}(x - 1)(x + 7)[/tex] ..(1)
To find x - intercept, plug y = 0 in above equation,
[tex]\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7[/tex]
Therefore, x = 1 and x = -7 are the x - intercepts.
Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.
So,
[tex]x = \frac{-7+1}{2} = \frac{-6}{2} = -3[/tex]
Plug x = -3 in equation (1)
[tex]y = \frac{1}{4}(-4)(4) = -4[/tex]
Therefore, the vertex is, (-3, -4).
The x - coordinate of the vertex is the axis of symmetry.
Therefore, axis of symmetry is x = -3.
Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
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Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios. A 2-column table has 3 rows. Column 1 is labeled Silver paints (parts) with entries 3, blank, blank. Column 2 is labeled Green paint (parts) with entries 4, blank, blank. Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check all that apply. 4:5 6:8 5:6 9:12
Answers
The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.
What are Equivalent Ratios?Equivalent ratios can be described as ratios that have the same values when compared to each other. For example, 8/16, 4/8 and 1/2 re equivalent ratios because:
8/16 = 1/2
4/8 = 1/2
Therefore, 8:16 = 4:8 = 1:2.
Given the table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, the ratio is: 3:4.
This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.
Therefore:
6/8 = 3/4
9/12 = 3/4
6/8 = 9/12 = 3/4
This implies that 6:8, 9:12 and 3:4 are all equivalent ratios.
Therefore, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.
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