Answer:
[tex] - \frac{x + 2a}{3a + x} [/tex]
Step-by-step explanation:
[tex] \frac{ {x + ax - 2 {a}}^{2} }{3a {}^{2} - 2ax - {x}^{2} } [/tex]
i) write ax as a difference
[tex] \frac{ {x}^{2} + 2ax - ax - 2 {a}^{2} }{3 {a}^{2} - 2ax - x {}^{2} } [/tex]
ii) write -2ax as a difference
[tex] \frac{ {x}^{2} + 2ax - ax - 2a {}^{2} }{3a {}^{2} + ax - 3ax - x {}^{2} } [/tex]
iii) factor out x from the expression
[tex] \frac{x(x + 2a) - ax - 2 {a}^{2} }{3 {a}^{2} + ax - 3ax - {x}^{2} } [/tex]
iv) factor out -a from the expression
[tex] \frac{x(x + 2a) - a(x + 2a)}{3 {a}^{2} + ax - 3ax - {x}^{2} } [/tex]
v) factor out a from the expression
[tex] \frac{x(x + 2a) - a(x + 2a)}{a(3a + x) - 3ax - {x}^{2} } [/tex]
vi) factor out -x from the expression
[tex] \frac{x(x + 2a) - a(x + 2a)}{a(3a + x) - x(3a + x)} [/tex]
vii) factor out x+2a from the expression
[tex] \frac{(x + 2a)(x - a)}{a(3a + x) - x(3a + x)} [/tex]
viii) factor out 3a+x from the expression
[tex] \frac{(x + 2a)(x - a)}{(3a + x)(a - x)} [/tex]
ix) factor out the negative sign from the expression and rearrange the term
[tex] \frac{(x + 2a)( - ( - a - x))}{(3a + x)(a - x)} [/tex]
x) reduce the fraction a-x
[tex] \frac{(x + 2a)( - 1)}{(3a + x)} [/tex]
[tex] - \frac{x + 2a}{3a + x} [/tex]
Given the set of vertices, determine whether parallelogram ABCD is a rhombus, rectangle or square. List all that apply. A(7,-4), B(-1,-4), C(-1,-12), D(7, -12)
a. rhombus c. square, rectangle, rhombus
b. square d. rectangle
Given:
Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).
To find:
Whether the parallelogram ABCD is a rhombus, rectangle or square.
Solution:
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]AB=\sqrt{(-4-(-4))^2+(-1-7)^2}[/tex]
[tex]AB=\sqrt{(-4+4)^2+(-8)^2}[/tex]
[tex]AB=\sqrt{0+64}[/tex]
[tex]AB=8[/tex]
Similarly,
[tex]BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8[/tex]
[tex]CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8[/tex]
[tex]AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8[/tex]
All sides of parallelogram are equal.
[tex]AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}[/tex]
[tex]BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}[/tex]
Both diagonals are equal.
Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.
We know that, a square is special case of rectangles and rhombus.
So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.
anyone know this two questions I can't figure this out
Answer:
22) x - 46 = 74
23) 20 portions
Step-by-step explanation:
21)
Let x = the number of cars Sara sold.
Jerry sold 46 cars fewer than Sara, so Jerry sold x - 46 cars.
Jerry sold 74 cars, so the equation is
x - 46 = 74
Answer: x - 46 = 74
22)
Let the number of 1/3 lb portions = x
The weight of x number of 1/3-lb portions is 1/3 * x, or simply x/3.
The full bag weighs 6 2/3 lb.
The equation is
x/3 = 6 2/3
Now we solve for x.
x/3 = 20/3
Multiply both sides by 3.
x = 20
Answer: 20 portions
Answer:
let 's' = Sara's amount
let 's-46' = Jerry's amount
equation: s - 46 = 74
s = 120
Step-by-step explanation:
2nd question: [tex]\frac{20}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{20}{3}[/tex]· [tex]\frac{3}{1}[/tex] = 20
Help with this problem!!!!
X/2-3=9
Answer:
pretty sure it's
2
−
3
=
9
\frac{X}{2}-3=9
2X−3=9
2
−
3
+
3
=
9
+
3
A study has shown that the daily amount of milk produced by a dairy cow is normally distributed, with a mean of 6.2 gallons and a standard deviation of 0.7 gallons. On a given day, 99.7% of the cows will produce an amount of milk within which of the following ranges?
Answer: 4.1 gallons to 8.3 gallons
Step-by-step explanation:
just took the quiz
99.7% of the cows will produce an amount of milk in the range is 5.5 gallons to 6.9 gallons option (A) is correct.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
The missing options are:
A. 5.5 gallons to 6.9 gallonsB. 4.8 gallons to 7.6 gallonsC. 4.1 gallons to 8.3 gallonsD. 3.4 gallons to 9.0 gallonsWe have:
A study has shown that the daily amount of milk produced by a dairy cow is normally distributed, with a mean of 6.2 gallons and a standard deviation of 0.7 gallons.
The mean = 6.2 gallons
Standard deviation = 0.7 gallons
The range can be calculated:
Lower range = 6.2 - 0.7 = 5.5 gallons
Upper range = 6.2 + 0.7 = 6.9 gallons
Thus, 99.7% of the cows will produce an amount of milk in the range is 5.5 gallons to 6.9 gallons option (A) is correct.
Learn more about the normal distribution here:
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L.B Johnson middle miguel took part
Answer:
Johnson Middle School held a track and field event during the school year. Miguel took part in a four-person shot put team. Shot put is a track and field event where athletes throw (or "put") a heavy sphere, called a "shot," as far as possible.
Step-by-step explanation:
PLZZ MARK BRAINLIEST!!!!!
how many men have a waist measurement of more than 85cm
Answer:
29
Step-by-step explanation:
How do you rotate triangle A",B",C" 270 degrees around the origin. coordinates A" (-1,1), B"(1,-2) and C"(0,-4)
9514 1404 393
Answer:
rotated vertices are (1, 1), (-2, -1), (-4, 0)
Step-by-step explanation:
When the rotation direction is not specified, it is usually taken to be counterclockwise. Rotation 270° CCW is the same as rotation 90° CW. The transformation of coordinates is ...
(x, y) ⇒ (y, -x)
Then your rotated points become ...
A(-1, 1) ⇒ A'(1, 1)
B(1, -2) ⇒ B'(-2, -1)
C(0, -4) ⇒ C'(-4, 0)
_____
In the attached, the rotated triangle is shown in red. As an example, the arc through which point C is rotated is shown.
Find the mean, median, and mode of the data set 8 2 7 2 6 5
Answer:
Mean is 6, median 5.5, mode 2
Step-by-step
Answer:
mean=8+2+7+2+6+5
=30
30÷6=5
note: divide the total with it's sum.
median=7+2
=9
9÷2= 4.5
note: median is the middle no. since there is no middle no. so just add those two no. and divide it by 2.
mode= 2
since it occurs twice
How many 1/2 yard lengths are in 1 yard
Answer:
1/2 yard is equal to 18 inches
Step-by-step explanation:
What is the value of the expression 24/x when x = 8?
Answer:
Itd be 3 becaus 24/8 is 3
There are six doors in a hostel .In how many ways a student enters the hostel and leave by different door
Answer:
5 times
Step-by-step explanation:
Because he enters through the front door.
Find all the real square roots of -49
Answer:
-7
Step-by-step explanation:
Answer:
7i
Step-by-step explanation:
the square root of 49 is 7
i equals -1
7 squared times -1 equals -49
xoxo,your highness...While President, Obama received an average of 60, 000 letters per week at the White House.
Approximately how many letters does he receive in a day?
Answer:
8571 letters per day
Step-by-step explanation:
60,000/1 week is the same as 60,000/7 days so
60,000/7 = 8571.428571
is aproximately 8571 letters per day
Which statement about the value of x is true?
O x>38
Ox<39
Ox=77
OX > 103
Answer:
x = 77 and x > 38
Step-by-step explanation:
Sum of all angles in a triangle is 180.
The angle PNO will hence be:
180 - 38 - 39 = 103 degrees.
The angle PNO + angle x = 180 degrees (straight line)
So 103 + x = 180, therefore x = 180 - 103 = 77.
Which is also greater than 38, so x > 38 is also correct.
The solution is : x = 77 and x > 38
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
Sum of all angles in a triangle is 180.
The angle PNO will hence be:
180 - 38 - 39 = 103 degrees.
The angle PNO + angle x = 180 degrees (straight line)
So 103 + x = 180,
therefore x = 180 - 103 = 77.
Which is also greater than 38,
so x > 38 is also correct.
To learn more on angle click:
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Please help me answer this !
Answer:
[tex] y = -\frac{1}{2}x + 4 [/tex]
Step-by-step explanation:
The equation of the line can be written in slope-intercept form, as y = mx + b.
We need to find the slope (m) and the y-intercept (b) of the line, then plug their values into the slope-intercept equation, to find the equation of the line shown.
y-intercept (b) = the point where the line intercepts the y-axis = 4
Using two points on the line, say, (0, 4) and (2, 3):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 4}{2 - 0} = \frac{-1}{2} = -\frac{1}{2} [/tex]
m = -½.
Substitute m = -½, and b = 4 into y = mx + b.
The equation of the line would be:
[tex] y = -\frac{1}{2}x + 4 [/tex]
Hello there ^^ I'd love it if you would help me :D
Answer:
Great question
Step-by-step explanation:
Where is it :p
what percent of 30 is 16.5..................................
HELP!!!! 2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
The dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching television each week. What are the mean and median?
The 5th-grade mean is
.
The 7th-grade mean is
.
The 5th-grade median is
.
The 7th-grade median is
.
Answer:
5th grade mean - 4.67
7th grade mean - 3.46
5th-grade median - 5
7th-grade median - 3.5
True or false
2+(-2) is equal to zero.
Answer:
It is TRUE.
Other:
Brainliest? Thanks!
A circular tablecloth has a diameter of 6 feet,as show on the picture.
What is the area,in square feet,of the tablecloth.
one and two-thirds divided by 3
Answer:
5/9
Step-by-step explanation:
Simplify fractions
3\10
1/8
Answer:
Already simplified
Step-by-step explanation:
Answer:
Step-by-step explanation:
its preety simple you just have to divide 3/10 and 1/8 and you will get your two answers
A principal purchased a total of 32 gas cards and movie passes for prizes. Each gas card cost $25.75, and each movie pass cost $7.25. If the principal spent a total of $454.00, how many gas cards did the principal purchase?
Answer: 12
Step-by-step explanation: 25.75a+7.25b=454
a+b=32
will give bralist HELP ME PLEASE
Answer:
It would be a I think
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
In a right-angled triangle
, one acute angle is 30°. Find the other acute angle
VII CLASS MATHEMATICS
Answer:
60°
Step-by-step explanation:
sum of all angles is 180
and it's a right-angled triangle so there is angle = 90
so the other acute angle = 180-30-90=60°
Answer:
60
Step-by-step explanation:
90+30= 120
180-120= 60
Louis is buying groceries and stops at the deli counter to purchase sliced Swiss cheese. The deli uses a scale like the one shown to calculate the weight and price of deli purchases.
Which relation below is not a function
Answer:
its c i believe <3
Help I’ll mark you brainly! And give extra points!
Answer: I think #2 is either A or C
Step-by-step explanation: Hope it helped! :)
backpacks originally cost $24 but if 40% back to school sale is going on determine the sale price of the backpack.
I need help right now
Really Important!!!!!!!
Answer: The price is now 14.40
Step-by-step explanation: The difference is 9.60
Solve for x. Round to the nearest hundredth. ?!?!? Please HELPP ASAP
I really don't know this I'm so sorry
Answer:
14
Step-by-step explanation:
Well, a right triangle has a total of 90 degrees, if the hypotenuse is 22, and leg b is 54, then the remaining leg a would have to be 14.